One of the area's favorite traditional bike events is coming this Friday, the Medina YWCA's July4 Twin Sizzler Race.
You can enter the 5K or 10K running race/walk, bike race, or both.
The bike race has an Expert and "Citizens" (i.e. beginner) division. It's a good, challenging 27-mile ride, and a good opportunity to test your racing chops even if you don't usually race.
You can find the full details online here. The registration link appears to be broken; I sent them an e-mail to let them know, so maybe it will be fixed soon.