A good friend of mine lives in Terre Haute and I have been to Rt 66 with him and we drove by Gateway on our way to St Louis. If memory severs correct Gateway is about 3 hours away from Terre Haute and Rt 66 about 3.5 hrs. Gateway is pretty much a straight shot down I-70. Rt 66 will require a few more turns, but still easy to get to. Terre Haute has an 1/8 mile track as well.
As Tony said above go to IMS. I have not been for a race, but went for the tour. I am not a big Indy car fan but was amazed at the track itself. It was the first time I had even driven through a tunnel under a track. Quite a rush when you get to the other side and you an in the speedway. Any motorsports fan would enjoy it. My friend who was not a race fan before he moved to IN has been to quite a few events at IMS, from qualifying, to carburation day, to the 500 itself.