There's quite a bit to do. The bad part about St. Louis is that the stuff to do is kind of spread out. Just avoid East St. Louis (not that you'll be going across the river anyway), and North St. Louis.
I'm assuming you're coming into town for a Cardinals game. There's a few bars around the ballpark that are pretty packed after the games. I'd head down to Washington Street, and hang out there. Lots of bars, and open patios.
The Landing on the riverfront has some decent restaurants.
Delmar Loop has Fitz's bottleworks, Vintage Vinyl, and some other shops that are pretty good. The Pageant is also there, one of the best venues to see music.
The Zoo is fun, and its free.
Just to be forwarned, summers here flat out suck. I'm used to them from living here all my life, but its very high humidity. Ever wear a sweater in the heat? Its about like that.