Autocrossing is done basically anywhere people can make a course. I've been on airports that have been converted to road courses. SVTCole (I think) rolled his car while on a Go-Kart track. What really defines Auto-cross Solo II (there are different types, but that is the one most people mean) is defined by 1 car at a time, single timed runs. The course is laid out in such a way as to limit your top speed to under 60 MPH. It's part drag-race part road-course. It's a blast and you can do it with just about any car you can get to pass a minimal safety inspection. You also don't get to drive the course very often 3-8 runs in one day (run = 1 lap) so it sharpens your driving skills very quickly. You have to learn how to set up for turns and brake etc etc with almost no practice and still make very fast times.
Hope this helps.