Scenic Hills and Berlin RV are near Berlin, Ohio. Both are what some might call parking lots along with Evergreen in Mount Eaton. Amish Country Campsites is north of Winesburg a spit but sites are small with no activities area for children. The closest to a "campie" would possibly be Meadow Lake Campground just north of Wooster. Been a while since I've been there, (too close to home) but some campsites are in the woods. There is a swimming pond there and I think a fishing pond. Millersburg is approx 30 miles south with Berlin, Kidron, Orrville, Wilmot, Fredericksburg, Maysville, Applecreek, all being a shorter distance and within 30 minutes. Sugercreek is a little farther.
Ah! Found their website so check it out
HERE. Just thot of another campground is
Whispering Hills. and
Camptoodik. There are others if you go to Mohican area but can't remember them all.