The best deal in St. Louis - if they're still offering it - is at the Chase Park Plaza on Kingshighway. The building has been there forever and houses long-term rentals, but they have a small section that's recently been renovated into single night stays. The times we've stayed there, it was $139 a night for a brand new one bedroom condo fully furnished with kitchen, utensils, etc. It's directly across the street from the park, and very close to the Science Center. It's in the Central West End within walking distance to lots of restaurants (with outside seating) and shops. As you might imagine it's VERY difficult to get a room there, but definitely worth the effort.

Agree with the above poster -- I stayed there for a wedding last summer and it was great! They have a lovely pool. We had a room with a full kitchen that had just been renovated. It is right across the street from the attractions you mention, and there is a movie theatre right next door. The hotel has valet parking for a fee but we parked our rental car right on the street in front of the hotel and had no problem. If the search function is working you should be able to search and find my detailed post about our stay there, that also listed other things nearby like a nice gourmet food market, fun neighborhoods for restaurants and antiques, etc. Also, if I remember correctly I believe the hotel has a website so try a search engine using the name.