Originally posted by: DrPizza
Gateway arch in St. Louis? Bah. If you've seen one inverted hyperbolic cosine monument, you've seen them all
It's actually an inverted catenary...
I've lived in Dayton for five years and right near Indianapolis for the previous 18, now in St. Louis for the last 2. I'd recommend the following:
1. USAF museum - just west of Dayton near WPAFB (about 5 mi. south on I-675). Not too expensive and really interesting. I used to work in one of the buildings about half a mile up the hill from the museum in the base. If I still did, I could sneak you in and show you some of the things that will be in the museum about 50 years from now.

2. Walk around downtown Indianapolis. Not a whole lot of sight-seeing that I would recommend other than maybe the Children's museum (#1-2 in the country) that a science-dork like you might enjoy (saying this as a fellow dork-in-arms)
3. Anheuser-Busch brewery in St. Louis. Free tour, free samples. I'm not a big fan of their products, but free beer is always a plus. The Schlafly brewery is also in St. Louis, but I don't recommend it. The zoo is top-notch and free, as is the art museum and science center (all in Forest Park). The Loop (on Delmar) is a common tourist trap, but I can't really recommend it. I can also give you a free tour of the engineering facilities and med school at Washington University.
4. World's largest McDonalds (I think it's north of Tulsa on I-44?). It spans the interstate - hard to miss. Has a gift shop with Route 66 stuff, but not much to really see here. I just included it because it's the only thing of note on I-44 in that part of OK.
Also a couple pointers... Don't speed too much in Ohio. The cops there are bastards and will ticket you for going <5 over. Good news is that they are required to have their headlights on if gunning at night. Also, beware the drivers, especially around Dayton. Indiana and Illinois have unmarked/undercover highway patrol cars, especially Camaros and Mustangs. Don't speed in Illinois construction zones, as the fines are insane and they really do enforce them. Bypass St. Louis on I-270 unless you're going into the city for anything. Traffic sucks because they're reconstructing the bridge that carries I-55, I-64, I-70, and US-40 over the Mississippi. If you need help finding a place to stay/eat along the way, PM me and I can make some recommendations. I've driven every inch between Dayton and St. Louis at least ten times, and I-44 from St. Louis to Tulsa once.