Any serious look at themed attractions has to look at zoos, and to use the popular urban parlance, "Ohio's zoo game is strong." Columbus Zoo also operates The Wilds, a gigantic outdoor animal facility south of Zanesville. Consisting of some 20+ square miles, The Wilds is roughly half the size of Walt Disney World's entire boundaries, and multiple times as large as the next largest facility (San Diego Safari Park). In addition to bus and jeep tours that run near 2 hours, there's ziplines, rental yurts for overnight stays, and onside dining. Don't forget the pollinator garden either.
Not as well known as Cincinnati or Columbus, but not much less grand, are Cleveland and Toledo's zoos. Cleveland Metroparks Zoo has an outstanding Australia area with train ride, classic carousel, and the impressive indoor Rainforest area. Toledo has two carousels, a train that runs the perimeter of its well done "Experience Africa" area, and an aerial course, as well as some really good WPA structures that still stand. The other small cities of Ohio still have above average stuff for zoos: Dayton's Boonshoft Museum of Discovery has an AZA accredited indoor zoo within a science museum. Akron's zoo is small but still has a carousel (and a "train"; doesn't really run on track) and impressive theming in sections like Grizzly Ridge.
Some of the most traditional amusement vibes on the planet can still be found in Ohio. Stricker's Grove is a throwback like almost no other; it's a private picnic park for group outings that opens to the public only a few days a year. While many picnic facilities exist in the US, few contain two operating wood coasters and an assortment of classic flat rides. Stricker's has the business model and the ride selection of something from the 1950s, except you can see and experience it in the present day. Interesting fact too: during our last visit at Stricker's in 2017, I flipped arcade play into a Vollmar's Park trivet, of all things. Vollmar's Park operated several hours away in Bowling Green and actually closed in 2001. Maybe some of the rides had wound up here at Stricker's, but I still found that a really strange find.
The state also features two classic 50s era kiddie parks. Memphis Kiddie Park operates on a small plot of land in Cleveland proper: the Herschell Little Dipper coaster at the park is among the oldest steel coasters in the world, having opened back in 1952. Another Herschell kiddie coaster can be found at Tuscora Park in New Philadelphia, half an hour south of Canton. Unlike Memphis Kiddie Park that is family owned, Tuscora is a public park which has outsourced amusement operation to a third party to draw families. The rides are geared to kids and in many cases exclusively open to them.
Newer family entertainment center style facilities have popped up to help take some of the load off. The owner of Howard's Apples Farm Market acquired a kiddie coaster from the defunct Dover Lake Water Park, then decided to open it to guests coming for apple cider slush and corn mazes in 2016. An hour south of it is Sluggers and Putters, an above average mini golf/go kart facility who opened a refurbished version of Americana's old kiddie coaster in 2015. While it possesses no rides, Entertainment Junction north of Cincinnati does have trains - so many in fact that it has the largest indoor train display in the world. Part of it? A model of Coney Island Cincinnati.
When a name became popular in the 19th and 20th century, everyone raced to copy it. When getting into hot water became popular, a lot of "Carlsbad"s started to come around. When amusement parks started getting built, everyone wanted a name that screamed what it was you were attending. RCDB lists 21 amusement parks named "White City" after the original 1893 World's Fair. There's 14 Dreamlands, 13 Tivolis, 10 Coneys, and 124 Luna Parks. Those are just the places that ever had a roller coaster, by the way. Coney Island Cincinnati was one of these places. It's not on an island, but it did have a swimming beach (later replaced by a pool, probably since the Ohio River wasn't the best to swim in), and it did have rides. Lots of 'em. It was among the most, if not the single most, successful regional park in the United States after World War 2. Walt Disney himself sought out the advice of its owner and manager, Ed Schott (yes, like Marge, who married into the family) when developing Disneyland.
Coney Island was too successful for it's own good: that position near the Ohio River that once brought in steamships full of passengers also meant the park was in a flood plain. There are also rumors that pressure either from within the ownership or from outside in Cincinnati's elite pushed the ownership (which by this point had morphed into Taft Broadcasting) into moving Coney Island. The park was supposed to close forever after the 1971 season; one which was reportedly its most successful. After only a few years of limited operation, Taft wound up spinning off Kings Island and keeping Coney Island. The park was ultimately sold in 1991, and while it is nowhere near as grandiose as it once was, many features such as the Sunlite Pool (largest recirculating pool in the world since opening almost a century ago), modern and classic thrill rides, and even a steel roller coaster still run.
As amusement parks have closed, many Carousels have been made available and become standalone attractions. Among the most notable are the two at Sandusky's Merry Go Round Museum, which is downtown only minutes from Cedar Point. There's displays, horses and other figures to view, and then of course the carousels themselves. The Cleveland History Center recently reopened a carousel of their own, this time once owned and operated at another venerable Ohio institution that closed in the 60s; Euclid Beach.