There are a lot of flea markets in the Ashtabula County area. The best one they have though to me is the one in Andover, Ohio. It is all outside vendors at this really old drive-in. Tons, and tons of vendors and everthing you can think of under the sun is there.
Rogers open air market in Rogers OH (south of Youngstown)is excellent. Open on Fridays year round...HUGE and a ton of vendors. I've found everything from antique furniture to fresh garden vegies...great food vendors also... try www.fleamarketguide.com/oh