Yeah, pretty much works like this...
Best place in the city to hang out is the Clayton/Forest Park area. It's by far the nicest, and it holds the Zoo, which has been mentioned many times above.
Chesterfield is also real nice, but it can get to be a bit far out.
Downtown St. Charles and the surrounding area has a couple very nice Casinos, including Harrah's and Ameristar, and as mentioned above, an old town style shopping district. A really fun place to eat and play over in this area is Dave and Buster's. They've got great food and a Disney Quest (without the virtual reality) type of play area geared towards adults.
Worst places to go, or should I say, places to avoid:
East St. Louis - Bad, bad things over here. Basically it consists of the immediate area, and then up to 5 miles away on the Illinois side of the river.
The immediate North and South areas just outside of Downtown St. Louis are in pretty bad shape when it comes to cleanliness and the type of people as well.
Like most cities, there is a fine line or road where things tend to change to the point where you don't have to be scared to walk down the street. The closest thing we have to that street here in St. Louis is either Kingshighway or Hampton. Both of them run perpendicular to Interstate 64/40. This is the highway that runs directly west out of Downtown.
For nice places to eat, it depends on your budget, but there are quite a few nice dining options in the immediate Clayton area. One of my favorites is J. Bucks, which refers to the late Jack Buck, and then his son and daughter Joe and Julie. It's slightly upscale, but still relaxed, and the price doesn't show it much at all.
As mentioned above, Kirkwood has a nice Old Town feel in a certain area, and then there's also "The Hill," which is probably the most famous area of St. Louis for good eats.
I think that's about all I can give you off the top of my head. Hope it helps!