I'm not a race fan, but I've lived here 13 years and can't escape Indy 500 mania.
We usually end up bringing out of town guests to the track. You can even drive around the track if you want to pay for the priviledge on days there isn't any racing activities.
There is a golf course in the center, if you're into that.
The thing that bugs, however is that my friend just wanted to get a Tshirt. Not interested in the museum or the track, just the gift shop. They wanted to charge her admission for the gift shop!!
We found an Indy 500 Tshirt at the mall and called it a day.