Every Thursday night there is a cruise-in at Wholly Joes(hot dog,coney joint) on Polaris Parkway, east of rt.23 and west of I-71. Roughly 6pm-9pm. Every Friday night, there is a group of rodders (unorganized) that meet at Yogi's Hoagies on rt. 3c, just north of I-270 about a mile. Also roughly 6pm-9pm.
If you want to drive a couple of hours the Brimfield Hot Rod Nats is this weekend in the Akron area. I've never been there but it looks like a good show. http://www.jalopyjournal.com/forum/showthread.php?t=739373&highlight=brimfield