Thanks to your guys' advice and wisdom, I finally attended my first autocross at the Lorain County Speedway, about 45 minutes west of Cleveland. I had an absolutely fantastic time, and the beater Sentra took everything I could throw at it without even complaining.
The track was set up as something of a figure eight, with a slalom on one of the banked turns. I had 7 runs, cutting my time down from 66 seconds to 53 by the last run. I came in dead last, but with a smile on my face that won't be going away anytime soon. I met some really cool people with even cooler cars, and I'll be going back any chance I get.