I think stock car or NASCAR wouldn't be the best. I think horse-racing in general would be better. Horse-racing is very popular sport. Hundreds of families raise the best best breeds for racing. In the south, in the Midwest, even in New england horse-racing is popular. And to me, it would be more likely to survive the apocalypse than stock car racing. I think a general horse-racing tournament would be good for nearly all of the US cultures.
Don't know how the event will go, but it would go like the tournament except it relies on the horse you use. The better the horse, the more likely you'll win/get better rewards. But it will also mean the more expensive the horse will be.