Here's a link to Van Buren State Park (dogs permitted)

http://www.dnr.state.oh.us/parks/parks/vanburen.htm

Van Buren State Park
Location: 12259 Township Rd. 218
Van Buren, OH
Correspondence and Phone Inquiries:
Mary Jane Thurston State Park
1-466 State Route 65
McClure, OH 43534-9711
(419) 832-7662

Van Buren offers a campground with 40 non-electric sites. A multi-use campground at the east end of the park offers 38 non-electric sites for general camping as well as horseman's camping.
Tables, pit latrines and a dump station are provided. A primitive, walk-in, youth-group camping area is located in the southeast section of the park and is available by reservation. Pet camping is permitted on designated sites.