In St. Louis definitely visit the Arch...it's a sight to see.
Also, I really enjoyed City Museum...it's a whacky little place with some science stuff, some oddities and you can climb around the whole thiing. Not everyone's cup of tea, but I had a blast. I got some pics here: The Wierdest Little House in St. Louis
Oh, and if you need a pooch-friendly spot to stay I highly recommend Babler State Park
. It's got lots of green and hiking trails for the doggies and is not too far from town.