Alternate route. Take 70 out of the airport to 465 north. Two exits (?) up is Washington Street. Turn east on Washington and follow it into Downtown.
Potential parking opportunities:
Zoo
Turn right at Victory Field (baseball diamond) - there's a lot just under the bridge on the left side that I didn't know about until recently.
State parking garage is on the left; however, I don't think you can park there during the day. As a state employee, I beg you not to park there so we public servants can find parking (all the meters and other spaces we use when the garage is fill will be taken).
Also on the left is/used to be some underground parking. I think it's for a hotel.
Past the convention center on the right is an entrance for the mall parking.