Yeah!
I live in St. Louis so maybe I can help out a little bit.
First of all, which museum where you told about? The City Museum is like a giant playground built into an eight-story old city building. The art museum is farther out of the "downtown" area, but still centrally located.
1. Downtown (as in close to the arch) pretty much sucks. There is the ballpark, hotels, and resturants, but besides that, there's not really much to do as far as "entertainment" goes.
2. I would recomend the University City Loop. "The Loop" is a stretch of about seven blocks of unique stores and restaurants. There are two independent book stores, and independent theater, a record store, ethnic cuisines, and coffee shops. You should really check out Vintage Vinyl records. I go there around five times a week, so yeah. The STL "walk of fame" is also located on Delmar, the street which is considered "the Loop." The Delmar loop was voted as one of the "top streets in America" in 2007.
2. The "Central West End" is also pretty cool. This area is between forest park and downtown and offers a variety of resturants, coffee shops, and stores. I consider it a little more sophisticated than the loop. It would be an ideal place for dinner. Very cool old archetecture and a great local vibe.
3. Crown Candy is a really legendary diner in St. Louis that has been around almost as long as the city has. Unbelievable sundaes, cements, candies, burgers, and BLTs. Classic Americana in a really old resturant.
4. Forest Park- probably my favorite palce in St. Louis. Forest park is 50% larger than Central Park and has some really great attractions. This time of year it is really really beautiful! The art museum and the zoo are both located in forest park, and they are both FREE!
5. In a couple of weeks there is going to be a massive art fair that is thorughout the streets of Clayton, anotehr suburb.
Record Store Page Links:
http://vintagevinyl.com/
http://www.euclidrecords.com/
http://apoprecords.com/
Vintage Vinyl is my favorite, but Euclid has a much better selection as far as vinyl and used is concerned. Apop pretty much solely expirimental/noise as well as zines and tapes. Fucking cool place.
I would be glad to help and tell you anything else you need to know.