We visited the lovely Holden Arboretum in 8/05 and really enjoyed it. First we took a (volunteer)-guided tram tour for a nominal fee (reservations are recommended) - and later we took a tour of the Lantern Court gardens (reservations are necessary and there's a fee), which was a real learning experience and our (volunteer) guide provided a fascinating amount of information.
The Holden Arboretum is located about 30 minutes east of Cleveland and very near I-90.