Definitely City Museum. That place is lots of fun!
If you are into haunted locations the Lemp Mansion is interesting to grab a bite to eat at. The last time I was there with some friends (with permission) we were allowed to walk around as long as guests were not disturbed. This was towards the end of the night. I think they do formal walking tours as well.
http://www.lempmansion.com/
Pappy's has awesome BBQ - Take it to go unless you want to wait in a line.
http://www.pappyssmokehouse.com/
Caleco's is my favorite restaurant downtown - the menu is huge with something for everyone. It is open late. There is a model train that runs around the bar and huge fish tanks for scenery.
http://www.calecos.com/
Check out
Http://www.explorestlouis.com
You can see an event calendar there and a list of attractions that make St Louis awesome for having fun. Have a great trip.