Cleveland is ringed with municipal parks. http://www.clemetparks.com/recreation/hiking/index.asp If the weather is good, anyone of them has nice trails. I generally hike North Chagrin because that's pretty close to where I lived and I know the trails pretty well. South Chagrin has some lovely areas. These are suburban parks, but still nice. I did almost 6 miles in North Chagrin Friday, from Squire Castle to Buttermilk Falls. You would need to rent a car to get to any of these parks.

You can rent a canoe and float down the Cuyahoga (it won't catch on fire, I promise you). http://www.camphicanoe.com/ It's not great, but it's a way to get outside.

Holden Arboretum is also a nice place to hike. http://www.holdenarb.org/visit/directions.asp

That's sort of off the top of my head.