Type "St. Louis" into the text search box and you'll find lots of answers to this question.

A baseball game!!!

The arch of course comes to mind. Are you w/ kids? That puts a different spin on it.
There is a wine country about 30 min. away. There are quaint little winery's that produce some good vintages. ( Mo. use to be the largest wine producing states before prohibition.)
A tour of Bush Brewery is fun, there is a lot of beautiful historical buildings there, and the clydesdales stable is unbeleivable!
The central west end is a fun place to have dinner and check outh the Little boutiques.
Clayton offers upscale dining - some of the best restaurnats can be found here.
The zoo is one of the best in the world. It is a must-do, early in the day.
There are also many outdoor festival and concerts. Check a local web site, try google.com and type in what to do in st. louis on those dates
have fun

St. Louis has a world class zoo that both adults and children would enjoy. August would be a great time to go to the Muny outdoor theatre in Forest Park. Union Station is a unique place to see, but everything is overpriced there. The Arch of course. Grant's Farm (must have reservations). Lots of really great Italian restaurants on "The Hill".

If you have young kids, The Magic House (Children's Museum)is a must see.

If you are the least bit claustrophobic, do NOT do the Arch! I never realized that I was until I went up in the arch and nearly lost it. No thanks!

Union Station and downtown St. Louis are really neat. DO try to go see a baseball game. The stadium is really fun.

Bush Brewery and Grant's Farm are cool, too. The Clydes are awesome horses, and since it is still springtime, you'll likey get to see some foals, too.

Some of the posters forgot to mention that the St. Louis Zoo is FREE -- also Grant's Farm, and the brewery tour.

The baseball game and eating on "the Hill" are not.