The Speedway, home of the Indianapolis 500 motor race, is Indy's super-sight. The Speedway Museum features some 75 racing cars (including former winners) and a 500lb Tiffany trophy. Limited availability golf-cart tours of the grounds and track ($50) are available from March to October (OK, you're not exactly burning rubber in a golf cart, but it's still fun to pretend while you take a lap!).
The big race itself is held on the Sunday of Memorial Day weekend (late May) and attended by 450,000 crazed fans. Tickets ($35 to $125, www.imstix.com) can be hard to come by. Try the pre-race trials and practices for easier access and cheaper prices. The track is about 6 miles northwest of downtown.