OK, I grew up near STL, and I live in KC, and lots of people here come to me asking for things to do, so I have all kinds of things to offer:
Do you have kids? If so, the City Museum is incredible. As soon as you arrive and see the 4-story jungle-gym-type metal structure out front, you already know your kids are going to love it. I'd say that any kids aged 5 - 12 will love it, and possibly even older if there are younger ones to hang out with. Also, the extra $6 for the aquarium part is definitely worth it. It's my understanding that you can even pet stingrays and such.
The Zoo is one of the biggest and best in the country, and it's free, making it a must-see when you're in town.
The Arch is neat, but unless you're there when there's no line, DON'T go up in it... the lines are huge, and it's just not worth the wait. The stuff below the arch is pretty cool.
The Botanical Garden is cool, but I haven't been in years. Grant's Farm is also awesome - especially for kids as they can feed animals and such.
The Science Center is awesome, and if you have an inner kid in you at all, you don't need kids to join you to have fun there.
I only recently took the Brewery tour, and it was great. Here in KC we have the Boulevard Brewery, and it's a REALLY cool tour, but A-B has a lot more history, and it is simply MASSIVE. IMO, you can appreciate it even more if you go to a smaller brewer BEFORE you visit there, but it's not necessary. It's just incredible to see the difference in size of the two.
The casinos around STL are pretty good, but I'm not a gambler.
The
Delmar Loop or U(niversity)-City Loop is a good place to visit for a couple of hours to eat and hang around in, but won't keep you occupied for too long.
If you want to see a Cardinals game (if they're in town when you're there), you definitely should. I got to see the opening day game on the first day, and having grown up with the old stadium, I completely forgot about it from day one. The new stadium is just incredible, and gives a great view of downtown.
The city is as safe as any other major city, no worries. OF COURSE you'll want to stay away from the East Side, unless you want to see the strip clubs, and contrary to what some said earlier, PT's Sports Cabaret is a pretty good one. My "east side" story is that I have a friend that works in the STL area for an environmental company of sorts. He frequently has to go to sewers to look around for things. He went over there and was getting ready to head into the sewers, and some "gentlemen" on a porch started berating him for having a job. "Oh, look at your punk a$$. All proud cause you got a job. You're the man now, huh?" Of course his response was, "I'M GOING INTO THE FVCKING SEWER!" When he got out, they had stripped the tires off his truck and taken a lot of the tools. Luckily it was a company truck, and even more luckily, he had his cel phone on him to call someone to get the fvck out before it got dark.
If you need any more suggestions, as I've said, I've become a bit of an expert on STL travel tips, so just ask in here or PM me. I specialize in restaurant suggestions.