The track is outside of Austin. It's going to be a little bit of drive where ever you stay. I've only been to concerts there.
We generally stay at Oak Forrest, Lone Star, and Pecan Grove. McKinney Falls is a nice little state park as well. Oak Forrest is our favorite for doing things around Austin and it's about 15 miles from the Circuit of the Americas. Make reservations quick though. Pecan Grove RV park is pretty great, it is within walking distance to many restaurants, shops and a great little grocery store called Thoms Market. However it is closer to 20 miles from the track
We camp in a motorhome as well. Pecan Grove can difficult to secure a spot, however we did get a spot a little before Christmas for the fun of it. That one will fill quickly too.
Lone Star RV Resort is a Carefree park, used to be a KOA. It is right off IH35, about 10 or so miles from the park. We've stayed here many times too when we can't get into the others.
Guess it just depends on what you want to be around when you get back. If I could get into Pecan Grove I would, then Oak Forrest then Lone Star, but that's me. The state park is nice, but small, all dirt roads and such.
2015 Georgetown Forest River 351DS MH
2008 Keystone Cougar 293SAB 5th Wheel
2007 Jay Flight 30.5RLS 5th Wheel
2006 Jay Flight 29BHS TT