State parks are free! One of the best is Hocking Hills State Park, with fascinating sandstone caves and hollows. The park, about 55 miles southeast of Columbus, has hiking, fishing and nature programs as well as a visitors center. Highlights include 100-foot-high Ash Cave (left), Old Man's Cave, Rock House and Cantwell Cliffs.
Also nearby: Conkle's Hollow State Nature Preserve , a spectacular sandstone gorge with cascading waterfalls and 200-foot-high sheer cliffs.
Conkle's Hollow 
Cleveland Museum of Art The recent reopening of the renovated 1916 main building (left) and East Wing exhibition hall is only the first act in a long production. The museum's full makeover, priced at $350 million, won't wrap up until 2012.
Toledo Museum of Art The new Glass Pavilion houses a renowned glass collection and "hot shops," where visitors can see artists work.
Cincinnati Art Museum This institution has a special wing dedicated to the Queen City's own rich, artistic heritage, with more than 400 works including furniture, sculpture, ceramics and pottery, most made by artists born or trained in Cincinnati.
Kennedy Museum of Art, Athens This museum on the Ohio University campus features collections of Southwest Native American textiles and jewelry as well as contemporary prints.
Cuyahoga Valley National Park Just a half-hour south of Cleveland, the 33,000-acre park includes spectacular rock formations and waterfalls, 160 miles of trails and a living-history settlement that re-creates the society of Wheatfield Township circa 1848 (left).
Established as a recreation area in the 1970s to battle urban sprawl, Cuyahoga is now one of the nation's most accessible national parks. More than 3 million visitors come each year to the hilly, tree-filled park, bisected by the Cuyahoga River.
National Museum of the U.S. Air Force See more than 300 planes and missiles at the world's oldest and largest military aviation museum (left). Regular guided tours are offered daily; behind-the-scenes tours of the restoration area, where aircraft are renovated before being put on display, are offered most Fridays.
Magee Marsh State Wildlife Area This bird-watching enclave 30 miles east of Toledo has a boardwalk trail (left) and migratory bird center. These wetlands were part of a swamp that blocked regional settlement until it was mostly drained in the early 1900s.
Marblehead Lighthouse State Park The oldest active Great Lakes light and keeper's house stands on the tip of the Marblehead Peninsula. You can visit the grounds for free as well as a museum in the keeper's house; a small fee is charged for lighthouse tours.
Maumee Bay State Park Just east of Toledo, this lakeside preserve has a 2-mile boardwalk trail, nature center with interactive displays, two sand beaches, butterfly gazebo and other activities. Maumee Bay Resort is located in the park.
Ottawa National Wildlife Refuge Explore 10 miles of walking trails and migratory bird habitats through wetlands, forest and upland habitats.
Know of other free things to enjoy in Ohio? Add them in the Comments section below!