When you enter St Louis you come in via the state of Illinois. When you leave St Louis you are on Route 66 Missouri. St Louis for us was probably the "worst" city of the Route 66. I don't know what it was about the city - but for us it was a little disappointing and probably one of the only times we didn't feel safe on Route 66.
We stayed downtown in a chain hotel and our night in the city walked to the Gateway Arch to get a good sight of the city at night. For me this was great to see a city at night from on high - but I'm sure that in the day time the view would have been great. The ride to the top of the Arch is about $15 per person. As a word of warning - if you are claustrophobic this might not be one for you. You have to sit in a very very small pod with 4 other people and there isn't a way out until you hit the top!
Also worth doing in St Louis would be a river cruise. Sadly when we went the river was flooded and all the cruises were not running but certainly would be a great thing to do. The cost of this is about $20 per person.
As you leave the city of St Louis a stop at the Legendary Ted Drewes Frozen Custard - which is a local must!