If you love cosplay, make a cool costume and walk around "in character."  Maybe view it as acting?  

Waxahachie said something that befuddled me (that board games make up a majority of events) and that is not true; that said, I assume you meant they were the biggest single category, which I was certainly intrigued to see is indeed true.  But I mean, 6,564 Board Game events versus 4,377 Role-Playing Game events hardly tells me that the convention is overwhelmingly for board gamers (I have basically no interest in board games and Gen Con has been my favorite event since I first attended in the 1990s).

(If you were wondering, there were 11,362 non-board game events at Gen Con 2018 [RPGs included obviously])

One of my favorite things to do if you can find the time, is just walk around the con with no specific direction and take in whats going on. Every nook of the surrounding area of the ICC is filled with some sort of gaming. I still haven't hit all of the areas.

However, and correct me if I am wrong. The Exhibit hall seems to be overwhelmingly geared to board gamers. Yes there are sellers for RPG books, card games, costumes, and the art area, but it feels like the majority of the hall is board games. So that is something to keep in mind.

https://www.gencon.com/experience/spa

I don't have social issues so I cannot comment on what you would be going through in a place such as Gen Con. As others have said, the place is packed. The restaurants and hotels around the convention center will be packed. The streets will be full of people as well. While you are at the convention, unless you are in your own hotel room/vehicle, expect a crowd. I don't want to scare you off, but that is the life that is Gen Con. That being said, and I am not sure if this will help you at all, EVERY person attending Gen Con will have at least one thing in common with you! It's not like going to WalMart on Black Friday where everyone is out for themselves. Gen Con is different. We are all gamers of some type, and just about 100% of the attendees are just people who enjoy gaming and experiencing games with other people. For the most part, Gen Con attendees are much more polite, better behaved, and more than willing to speak with you about their game/hobby or leave you be if you so choose. As for social anxiety, there are others there who also have this, and some will tell you that because of the attendees and the nature of Gen Con they do not feel it as bad while others do not. If you have never attended, I would encourage you to go for it at least once. Don't schedule any events, just wander and see what is going on. Perhaps pick up some generic tickets just in case there is something that you discover that you would want to explore further. Take frequent breaks in some of the less crowded areas (2nd floor) or walk around the Center Circle Mall on the opposite end of the food court. Go to the museum across the street. Visit Lucas Oil Stadium and sit in one of the seats for a bit (they have about a quarter of the stadium seating on the middle level open during Gen Con, so I started taking a meal break there and relax for a bit. Hopefully, you will have a great time and be encouraged to come back year after year!

... That place is a living history museum and will do re-enactments of that era's life. Yes, I understand that a lot of the website and many internet testimonials are around educating school kids, but trust me, I've been there before (as a school kid, granted, but still, I've been there). It's not just for kids. There are multiple events held there - such as Symphony on the Prairie - that likely attract far more adults than young children. It's worth a visit if you're able to dig that era. 

Also, from a post in this Gen Con forum I remember seeing something about the Indiana Medical History Museum: https://www.imhm.org/. This one I don't know anything about, but the reviews in that thread seemed overall positive. 

And don't forget the museum that's actually right by the JW Marriott: The Eiteljorg. I'm always intending to go there myself, and I'm always too busy to free up the time. But if it's your thing, you may want to prioritize it. It is literally walking distance from the convention center, just across the street from the JW. 

You able to stomach newer stuff? The Indianapolis Motor Speedway has a museum dedicated to the Indianapolis 500: https://www.indianapolismotorspeedway.com/at-the-track/museum. Granted, you have to be an auto and racing geek to get into that, but if you are, then that's a good stop. Just seeing cars from before the 50's is crazy; you wonder what it's like to go fast in one of those little open-air things. 

One thing to note: So much of the tourist industry's emphasis on Indiana history is far too based on buildings and monuments. That's of course very interesting, but there's so much beyond that. I'm reasonably certain that the Indiana Historical Society (https://indianahistory.org/)has a far more encompassing view of experiencing history, and the big advantage is that their building is also not that far from the ICC. 

I know of many other things to visit, but Connor Prarie is already sort of far away from downtown (it's in Fishers, and it's a whopping 20-plus miles from the Convention Center). But things I'm familiar with are even further: The Levi Coffin house - one of the stops on the Underground Railroad - is all the way near the Ohio border, over an hour east. Metamora and Oldenburg (a pair of historical towns) are also nowhere near Indianapolis, let alone downtown. There's plenty in Indiana to see if you're a history buff. It's just that so much of it is scattered around the state. :(

I struggle with the crowds sometimes, and I make it a point to do several activities away from downtown to break up my days. I take a walk and have breakfast down at Amelia's in Fountain Square at least one morning, and last year I did the beer tour to be in a smaller group away from the ICC. Usually one night I will wander up Mass. Ave or back to Fountain Square as well to get dinner, though those places tend to still be busy at night, just with more non-gamers. I noticed that aside from the main floor on the "field" a lot of the side rooms at Lucas Oil tend to be less busy. I have definitely walked over there to get some air, then just read manga for an hour or two in the manga library to chill.

Even if you are only into a couple aspects of what the con has to offer, I still think there will be plenty to do. The emphasis is not e-gaming, but there are definitely still e-game events. I have a friend who is into CR and I would say at least half or more of her planned time at GenCon last year centered around CR stuff. There is, of course, tons of D&D stuff, but if you want to get in on a game, yes, you will almost certainly have to play with strangers unless you're going with friends and all snap up tickets to one session.

All else fails, there's the beer tent and plenty of bars around...that always helps me. :)

Additionally, to add to all of the very good comments, take a look at how many events take place in Lucas Oil Stadium.  A few hundred people in there on the field level is like nothing, so it doesn't seem as crowded as some of the other event spaces.
:)

If you feel the need to get away from the convention, there are a couple of excellent museums just two blocks northwest of the convention center:

The Eiteljorg Museum of American Indians and Western Art:
https://eiteljorg.org/
An extensive collection of visual arts by indigenous peoples of the Americas, as well as Western American paintings and sculptures.

The Indiana State Museum
https://www.indianamuseum.org/
The Lincoln Financial Foundation Collection in the museum is one of the most comprehensive collections of Lincoln artifacts.

Cheers!

Looks like you have gotten a lot of great replies here, but I will throw out one more. Lucas Oil Stadium can actually be a great place to decompress. There are a lot of events happening on the stadium floor and the lower level, but the place is so big that you can walk around the crowd without actually feeling crowded. Or if you need a break just hang out in the stadium seats and watch everything going on below, and you will have plenty of space around you. Its a great way to experience the feel without experiencing the crushing crowd. Just a thought from one crowd hater to another :)

I was new to Gen Con last year, and while my husband went with me, we play different types of games.  One thing I will suggest to you is Baldman Games D&D series.  I don't have issues with crowds or new people, but I loved playing with them.  I played the first session on Thursday morning and played with a great group of people.  Myself and three others decided to meet up on Friday and Saturday to continue to play together.  I heard of several others doing that as well.  I even added the extra session on and used downtime to level up my character.  The nice thing was that all of the games continued off of one another, so while they could be one shots, for me they were not.

Also, they have the D&D Experience, which I am going to try and do this year.  If you are able to do this you have the same DM and players at your table for 4 sessions.  That might take some of the stress off.

For the OP - yes there are crowds but you will never find a bigger family outside of GenCon.  You mention you're not into board games - when I first came to GenCon, that's all I did. After that I was into True Dungeon (you mentioned LARP, and this is literally a live action dungeon). Now tabletop role-playing? I still see this barrier of entry and I've only done it a couple times.  I don't want to be "that" guy and not know what I'm doing.  If someone like you knowledgeable in that area showed me the ropes, perhaps I could show you some of the awesome joys of heavier euros.  There are so many options and everyone is awesome.  Cheers brother - and have a good time.  

In response to the True Dungeon suggestion and reading some of the OP's posts regarding previous experiences and preferences, I would actually caution against True Dungeon, at least for your first time going to the con. While it could be considered a LARP, it is a pure dungeon crawl without any real roleplaying and even the opportunities you would have to interact with the volunteer DM's/NPC's are very fleeting at best. While it is something that many love (myself included), it can be a very emotionally draining experience just due to its fast paced and hectic nature as the True Dungeon team has really perfected the "Fog of War" experience.

Given the more crafty inclinations, I would however really recommend some of the cosplay and miniature painting lessons/crafting sessions that are offered. It varies from year to year what exactly is offered but the cosplay crafting lessons have definitely expanded over the years and they are always hands on with you walking away with a piece you made yourself based on what the lesson is focused on (i.e. chainmail or scalemail work, how to work with thermoplastics, etc.).

Also, if you do want to do some tabletop games, I cannot recommend the Legends of the Shining Jewel group enough. It is a Pathfinder living campaign setting using a unique world created by the folks that run it at Gen Con. They are a really great and inviting group of people overall with some fantastic GM's and their one shots are always all tied together somehow and great fun with a good balance of combat and roleplaying opportunities. 

I have run demos of card games and tabletop mini games at gencon, and played in several tabletop mini games and board games.  That is typically my jam.

I found last year that the Writers Workshop stuff is fantastic! (Medieval Feasts was a hoot!), plus they tend to be sub-20 person discussions and very interactive.

Most people here do not understand your level of social anxiety.

If you actually left DragonCon in literal tears and that post wasn't hyperbole, DO NOT come to GenCon. It's an even smaller space. 

If crowds bother you, book games over in Lucas Oil Arena.  Firstly it's not as crowded as the ICC, secondly you have a 288 foot roof and huge windows to dissipate the noise and alleviate the claustrophobia.

Nascrag has been running RPG tournaments at Gen Con for 40 years.  We do Pathfinder now, but we are pretty rules light roleplaying heavy.  If you know D&D you can play in our tourney.

We've been over in Lucas Oil for a while now and it's a mixed blessing.  Harder to attract players, but you don't have to yell to be heard.

LOS might be a good place for someone who needs some space.  The problem is that many events don't get assigned locations until well after they become available.  LOS seems kind of a dumping place for events that don't get space in the ICC, and especially for events that are submitted late.  So, when registering for events, he may not be able to pick them based on the location.

To the OP: Reading all the posts & responses, I would have to conclude that you might not really enjoy Gen Con, although it seems your wife would.  I don't know how far away from Indy you are, but if you can make it a day-trip, maybe just come for Friday or Saturday to get a feel for how things are.  This way, if you're really bothered by it, you're not out the cost of a 4 day hotel stay & having to change flights to head back.  Ease into it, and if it works for you, plan for 4 days next year.

My first "Con" Experience was also DragonCon in Atlanta, I was not impressed and put off atending conventions for 8 more years. 

GenCon is totally different from DragonCon.  DragonCon is a Partying Convention, GenCon is a Gamers Convention.  At GenCon no one will require you to fit in, you as a gamer already do, take the plunge and experience it at least once.  I think you will be pleasantly surprised , that even though this si a very lage convention and gathering of people, there is warm friendly atmosphere enjoyed by most.  That is not to say you wont have moments, the quiet room and the ICC 2nd floor are your friends when that happens( also bathrooms on the 2nd floor tend to be less crowded)

I have submitted a long 1st Edition Advanced D&D Event, on Saturday from 3 to 11PM,  It is an open world set in the old "Judges Guild" environment.  This will be my 4rd year running this and , 5 players from the first year returned the last 2 years.  The event is Snow Witches Continues.  DM Terrence "Terry" Hiett. Consider this a personal invite to join us for some old fashioned table top role playing excitement.

Terry Hiett aka "The DM"