Here's a link to the Cleveland Metroparks. There are several with hiking and other activities.

Also ditto the Holden Arboretum out east and the Botanical Gardens in University Circle. Both are currently open, but you need to make reservations in advance. They're also private so there is an entrance fee.

If you're in University Circle there are several museums, including the Cleveland Museum of Art and Natural History Museum. I believe both need reservations, too.

Downtown there's the Great Lakes Science Center and Rock & Roll Hall of Fame. If you're in town during the draft they may be closed (unless you're here for that).

If you head to the Holden Arboretum (or are east in general), there are several nice parks in Lake County. The Farmpark and Penitentiary Glen are close to Holden. Further east is the Girdled Road reservation.

And as others have said, the Cuyahoga Valley National Park is excellent.

I don't know if bike rentals are available yet, but if you're interested in biking you may want to check with some shops near the Towpath trail through CVNP.