I just moved to Cleveland and I came out to the Farmer's Market to get see what type of produce, etc they have. Wide variety of vendors with a wide variety of stuff. Veggies, mushrooms, fresh made pasta, meats, cheeses and the list could go on. Everything is fresh and locally grown, if that floats your boat. The only issue I have is how expensive things were, which is why I didn't buy all that much. $6 for a quart of strawberries seems a little on the high side to me!
In terms of parking, there are lots behind some of the shaker stores to take advantage of and some street parking along shaker blvd if you don't mind a little bit of a walk (with the nice weather of today, it was nice to enjoy it!). I plan to come back every so often