If its was me i would go with the Eastern suburbs, but after reading that you will be working mostly on the west side and in Akron i would stick w/the west or south sides. I'm biased towards the east side because i live near the Pa border in Warren and the far eastern suburbs are about 40 minutes from me. I've spent a lot of time in Mayfield, Solon, Chagrin Falls, Bainbridge, Beachwood, etc.
Also, if you're not used to a lot of snow the west side gets a lot less snow since the east side is in the snow belt.
I see you are coming from coastal NC. My brother relocated to Snead's Ferry about three years ago and he now lives in Jacksonville and teaches at Jacksonville High School. He loves the weather there and the job opportunities for him there, but he misses having concerts, sporting events and good shopping nearby. You'll get all of those things in the Cleveland area. Welcome to Northeast Ohio.
