Pack some snacks and enjoy a fun family day out at Dillon State Park. There's plenty of space for the kids to run about and get some exercise.
You're spoiled for sightseeing choice when in Ohio. Dillon State Park is an ideal place to start here, but there are loads of other fine places to visit. Dillon Lake, and Zane State College are near the outdoor recreational space and will fill in your day nicely.