We were in St. Louis for 2 1/2 days- mainly to see the Cardinals & tour the stadium- but found there is a surprising amount to do- especially things for kids

If you are there for more than a night - I would stay in Forest Park. There's a lot of restaurants, bars, and many activities are out there. We stayed near the Arch & the Stadium at the Robert Mayfair Hotel. It was awful and unsafe. It's inexpensive but I do not recommend it. I've posted a separate review on that. You really need a car as things are very spread out- especially in Forest Park.

Things to do:
Arch- if you don't do the movie- the whole experience is very quick- you are out in about an hour- the pod elevator that takes you up is very small- and the windows are small when you get up there- you really only spend about 10 minutes up there.
Stadium- we did a tour there which was good and you have to see a game there
City Museum- amazing museum with multilevel slides- great for all ages- even teenagers, on nice days there's an outdoor park on the roof that's supposed to be great
We tried to get to Candy Crown Kitchen- an old soda shop- but there was a long wait on the weekend- try on a weekday
If your child is a train lover- go to the Museum of Transportation in the suburbs. There's a train ride for the kids & many engines for them to climb on & a car exhibit- if you have time- they even have classes for small kids

In Forest Park
St. Louis Zoo was great- it's free- there's a petting zoo you can go to (we didn't have time for) but the train ride & carousel was a huge hit with our two year old
New Cathedral- A beautiful church with great detail- looks like it's out of Europe
We stopped in the Missouri Museum to see an exhibit on the World's Fair and stopped over at the site (the pavilion strangely was built after the World's Fair)
Turtle Park- giant turtle sculptures- fun for the kids to climb on
Jewel Box- the conservatory- was a beautiful little place to pop in and see
We ate at O'Connell's Pub- which we heard had the best burger- but it was just average
Pi - deep dish pizza- Obama had this flown into the White House for a party- go early as there are waits- really great pizza
Ted Dawe's- ice cream custard- good- but nothing to go out of your way for

We had a busy trip but most stops were pretty brief so we were able to see a lot.