Cleveland has one of the world’s best orchestras and one of the world’s best art museums, along with the natural history museum. There’s also a nifty children’s science museum, all basically in the same block.
Around Sandusky, there’s a bunch of water parks, including a Great Wolf Lodge. There’s a wide variety of tourist type attractions in there area, like the African Safari park where you drive through the animals.
There’s boating and beaches. You can take a ferries out to Kelly’s Island or the Bass Islands. South Bass was the site of a naval post during the War of 1812. There’s a big tower monument to Admiral Perry there in Put-in-bay - a nice little Great Lakes town. It commemorates the Battle of Lake Erie.
Out on Middle Bass Island, there’s a vinyard and winery. They have a resort out there now, too, called St. Hazard’s, but I’ve never been.
Those islands are about an hour by ferry from Sandusky. For a longer ride, you can head to Pelee island, which is in the middle of the Lake and is the southernmost point of Canada.
Cedar Point itself is maybe the best thing Ohio has ever done. The park has historic displays from a hundred years ago. They have a bunch of famous and historic carousels and some of the oldest operating rides around in addition to the latest thrills. If you’re a fan of amusement parks, you owe yourself at least one trip.