If you're at the Cleveland Clinic, you're probably closest to the Graeter's at Crocker Park, in Westlake. Westlake is about a 25 minute drive down I-90W. The Graeter's we went to is in Pinecrest, in...Woodmere, I think (or maybe Beachwood)...and is a little bit further out and involves a few more roads.
The first time I ever had Graeter's ice cream was when I went to Columbus with a high school friend to be her "model" as she took her state cosmetology exam. I still remember how good the mint chocolate chip ice cream was. Now my favorite dish at Graeter's is a single scoop of mocha chocolate chip topped with the bittersweet sauce. SO good! Yesterday, I went seasonal and had a scoop of the cinnamon ice cream...yum!