We live near St Louis and visit alot. At night St Louis can get a little sleazy but nothing too bad. We have never had any trouble there. Walking around during the day is fine downtown, but stick to the Metra at night or close by your hotel.
We love the Old Spagetti Factory but honestly its alot easier to get into at lunch time, we try to arrive just before opening and get seated immediately. Its really good food and not very expensive. Really a great value as most meals come with soup or salad, bread, iced tea/coffee and even ice cream. Oh and they offer carriage rides out front at night!
City Museum is AWESOME, we have been taking our girls for 9 years. Our oldest is 15 and still LOVES it! However you do have to be careful, there are lots of things to climb in, around, thru. And while we have had no accidents I have scolded my girls for being too daring and jumping off things too high. Also wear old clothes, especially bottoms as both my girls have ripped pants and shirts sliding off things. Most of the things there are made of rebar so thats what snags.