What's the best place to get, say, a two-liter bottle of cola near the convention center/downtown hotels?

I don't know if it's the best place, but there's a convenience store in the mall at the end with the food court (but on a lower level than the food court). Or at least there was the last time I was there. 

Depending on your definition of near there is a Kroger grocery store within walking distance of the convention center.  Maybe a half to three quarters of a mile walk straight north up Capitol Avenue to Michigan Street.

is the mall /mall food court still a thing? I thought they were closed...

I think you are thinking of Skymart One Ext

The last CVS downtown closed permanently after the BLM Riots

I think DGX is off Pennsylvania and its a pseudo convenience store 

Thx grandpa :)

Yeah I plan on hitting up the Kroger for essentials as soon as I get in, though I imagine that goes for lots of folks as well. I noted someone else saying that in previous years the Kroger looked like it had been looted even on Wednesday, so here's to hoping they're ready for the deluge.

One of my favorite activities throughout the year is investigating and buying new snacks and canned/bottled drinks to bring to Gen-Con. 

Granted, this technique does not really work if you are flying in, given the drinks are literally impossible and nobody is going to have too much room for snacks without paying for a checked bag! 

Having my car totally full between stuff to sell at the Auction and snacks and drinks definitely makes me feel ready and excited for the real deal.