Musuems: The City Musuem, The Art Musuem, and the History Musuem
Forest Park: There is so much to do in Forest Park. You can visit the Muny and see plays or even go to the St.Louis Zoo.
Merrimack River
Food to eat
Imo's Pizza: A STL classic that you must try if its the pizza or the toasted raviolis, its all good.
Gooey butter cake: No specific place is the best, but you have to try this STL classic.
Ted Drews: Again, a classic STL treat served cold, great for the warm STL days.
The Hill: The Hill is an Italian cultural area
Cherokee Street: Another cultural place with many authenitc Mexican dishes.
Experience
I live here, but I think it is such a diverse and exciting city. There is so much to explore and so much art and music in the city as well. You can be in the heart of the city and then 40 minuets later be hiking in Castlewood or kayaking on the river.