For a place to camp, check out Ebenezer Park in Rock HIll, SC about 20 miles south of Charlotte. It is about 5 miles from I-77. It is located on Lake Wylie. It is a very nice county ran park. Some of the sites have a lake view even though the campsites are about 100 yards from the water. They have full hook ups, free wifi, and playground. Nightly rates are about $25. I'm not sure of the exact rate, but it is +/- $5. About half of the sites can be reserved and about 1/2 are 1st come 1st serve.
As far as thing to do, those that others mentioned wil be good. Depending on when you are here and since you like racing, you may want to visit a local dirt track. Carolina Speedway on Friday night in Gastonia, NC or Lancaster Speedway in Lancaster, SC on Saturday. Both of these are about 30 minutes from Ebenezer Park.
We also have Historic Brattonsville which may be interesting for them. This is where Mel Gibons movie, The Partiot, was filmed.