There is much to do and see in St. Louis. We'll start downtown:
-Take in a baseball game. The city revolves around the Cardinals. Nearly everyone is in tune with how the season is going, or the latest news on the team. And with a new stadium, the question should be: Why not?
-The old courthouse downtown is one of the older buildings in downtown. If you're a history buff, then I'd recommend this, as you'll learn that it was the site of the Dred Scott case for freedom from slavery. And since it has been around since 1826, it'll be a good starting base to learn about the St. Louis history.
-No visit to St. Louis is complete without venturing into the gateway arch-the most recognizable piece of the skyline in St. Louis. This monument to Westward Expansion also provides a good history lesson. And wonderful views of both downtown and eastward into Illinois.
-Since you're downtown, and you've just learned a bit about St. Louis history, now it's time to explore. Next take a walk around "Laclede's Landing". This area of the city is immediately North of the arch, so you're not very far. As you may or may not have learned by now, this area was actually the birthplace of St. Louis. In 1763, a French fur trapper named Pierre Laclede, along with Auguste Chouteau, settled here and named it St. Louis, in honor of the patron saint of the king of France.
Now it is an entertainment hub. There are enough bars to keep one busy, a casino and plenty of eateries. The cobble stone streets and cozy, historical homes, and it's proximity to the city make this an ideal respite from the hustle and bustle of downtown.
-Not far is the burgeoning Washington Avenue, immediately west of "the Landing." This is the up-and-coming loft district of St. Louis. Once full of dilapidated buildings and poverty, this area now shows the wealth of the upwardly mobile caste. Hip, trendy bars now pepper the area, while new eateries are also beginning to appear. This is the area of the city where you sip a martini.
-On the opposite south side of the city you will find Soulard. Another historic district that offers plenty in the way of eateries and bars/pubs.
-Now we're moving West (probably west on Interstate 64/40 West) towards the Central West End. One of the more flashy corners of the city that amazingly doesn't lose that blue-jeans kind of feel. I wouldn't specify a main artery, but some main veins are Euclid, Maryland and Forest Park Parkway. To be quite honest, though, the area is quite pleasant to wander around, as there is a potpourri of both fine and casual restaurants (cafe Balaban is a St. Louis fixture (excellent jazz on weekends), while emerging favorites such as Liluma provide a dining experience with a little more panache), a few coffee shops (coffee cartel @ Maryland and Euclid is my personal fav). All in all, this is a pleasant area for strolls, dinner, coffee, movies (@ the grandiose Chase Park Plaza (where a piano player performs in each theater prior to the start of the show). But as with nearly everything in St. Louis, the prices aren't expensive, and you don't have to dress to the nines to enjoy this.
-Now you're not far from Forest Park, so you may as well take in some of the sites. If the weather is pleasant, then try taking in a show @ the Muny, an outdoor theatrical venue, or if you have kids, then try the zoo. There is a public golf course, as well as racquetball and tennis courts available, if recreation is your cup of tea. Or if you're in the mood to relax, then take out a paddleboat or promenade at the bottom of Art Hill.
If the weather lousy, then take shelter around some of fine pieces in the St. Louis Art Museum, or if you're curious about the place you're visiting, then try Missouri History Museum. All in all you could spend a day or a week exploring Forest Park, but I imagine most don't have that luxury.