I've camped in my motorhome at all three tacks that you mention, so I cannot tell you about showers at the various tracks. You should be able to put a blanket down at Gas City. Lots of seats at Lawrenceburg, so there's no problem there.

The IMS museum is worth the stopover - take a camera! And Speedweek is some of the best that you'll ever see!

Links:
http://www.gascityi69speedway.com/Track%202007.htm

http://www.lawrenceburgspeedway.com/faq.php

http://www.kokomospeedway.net/trackinfo.htm