Hi there,
Ohio has over seventy State Parks, each of them, offering lovely backdrops and lakes so, there is plenty of choice when it comes to
camping out in Ohio.
I would recommend Punderson State Park as it is located not far from the
city of Cleveland, and you would be able to enjoy
attractions such as the Rock and Roll Hall of Fame, Cleveland Art Museum, etc. It also offers amenities such as toilets, drinking water facilities, shower facilities, etc.
If you are traveling with the family, I would recommend the Indian Creek Camping Resort located north of Youngstown. It offers amenities such as heated pools, on site restaurant, etc.
To give you an estimate of camping sites prices, you are looking at something in the range of $18 upwards but it is best to check before you travel.
Hope this helps
VacationBuddy