Maumee State Park is gorgeous. Definitely worth taking the kids to! You can also camp not far from the beach, so if you're the camping sort ..
I was just at Oak Openings this past weekend - beautiful!
There is a Van Buren near Findlay.
Luna Pier, MI has a state park right off the lake, but the camping area lacked in my opinion. Flat, manicured lawn, young trees. There is some great playing in the water along the coast out there, though.
Also look up Ohio Festivals! (I did a google search last year and came up with a site that had a big list). For example, Grand Rapids, OH has an apple butter festival towards the end of the summer. Crafts, displays, etc. Not sure if your kids would like it, but I enjoyed it. And the Amish made apple butter was very good!
Going up into MI .. You have Brighton Rec area, Maybury Rec area, etc. All excellent parks.