http://www.nasa-southeast.com/
They are a great bunch of folks. A HPDE event is a great way to bring your own car and drive a racetrack.
A Cobra might be a problem without a full width rollbar. They may or may not let you run a single hoop, you can ask. They like to have the same protection for the passenger as well as the driver because you would have an instructor ride in your car. I think it's amazing that there are instructors that would ride in a Cobra at all. It would be a good opportunity to fit a full rollbar!