When you visit St. Louis, I highly recommend some of our totally free museums. We also have quite a few dirt-cheap museums. Most are less than $10. That's what, 6 Pounds?
Don't bother with the Arch, unless you like to look at a city from high up.
If you like art, The Art Museum (creative name, eh?)has a fantastic collection. Admission is free, although there is a fee for any special exhibits. The Art Museum is in Forest Park, which is kind of St. Louis' version of Central Park in New York. Forest Park is chock full of places to go, like The Muny, which offers 1,500 free seats for every show. They're not the best seats, so bring a pair of binoculars.
There's also The History Museum, The Jewel Box (an old greenhouse), and the Science Center.
The Zoo gets it's own paragraph, because the zoo is our pride and joy. Parking is $10 or so, but admission is (you guessed it) free! I went there a few weeks ago with my sister-in-law. We bought bracelets ($10) that let us in to all the pay attractions, all day long. So we rode the trains as long as we wanted, rode the carousel that's full of hand carved zoo critters, went on the air conditioned dinosaur ride, saw a (really crappy) movie, walked through a herd of butterflies, and visited the children's zoo. We were there for 6 hours! On a sad note, we're down to 1 polar bear. Both of his pit-mates dies recently. He looked very lonely. :(
If you're looking for something a bit more exciting, there's the City Museum; a touchy-feely museum that was once a factory. A mad man with some money bought the place and started building. It's still growing. Wear comfortable clothes, as you'll be crawling through caves and riding a 3 story slide. I particularly like the City Museum. Partly because everyone scoffed and said, "No one will pay to visit a museum!" and partly because they have a huge collection of St. Louis architecture. They've saved the facades and do-dads from practically every building that's been torn down. Since I grieve the loss of our old buildings, the architecture exhibit is my favorite place to go. The City Museum charges an admission fee, but their food prices are reasonable and the only other expenses are parking and the world aquarium. For $6, you can touch a non-stinging ray.
The height of excitement would be Six Flags St. Louis. Admission is $42, but they have specials all the time. Like any theme park, food is prohibitively expensive. Expect to spend $100 for admission and food. The thrill rides are thrilling, the other rides are fun, the water park is nice and wet... bring sunscreen. The water park hasn't been open long enough to grow decent shade trees. Six Flags is an easy 30 minute drive from Downtown St. Louis.
For that matter, just about everything is an easy 30 minute drive from downtown St. Louis. We're chock full of interesting places. The dog museum, the bowling hall of fame, horse racing, car racing, the delightfully haunted Lemp Mansion, the museum of transport for train fans, the Magic House for children, and so much more!
I haven't even touched on the people watching delights. Fun neighborhoods to shop and stare include the U City Loop, the Central West End (adjacent to Forest Park), Grand Center, and South Grand Avenue (I recommend Mokabee's Coffee House).
That's a month's worth of tourism, so take your pick!
We also have gambling boats.
You might wonder why so many of St. Louis' attractions are free, or super cheap. That's because we believe the arts should benefit everyone, regardless of income. A lot of our property taxes go toward our parks and museums so that everyone can enjoy them. The city is considering raising the property taxes again to support the St. Louis Symphony. When the measure finally comes up for a vote, I bet it'll pass. I'll happily pay another 2 cents per hundred dollars of valuation to maintain our world class symphony.