One of my favorite things about living in Cleveland is the West Side Market. It is an experience that you can't find very many places. Both the produce and the meat section are huge and buying produce at the market will usually save you money from a grocery store AND you will get better quality food! Win win.
Come here and spend the afternoon, it's fun. You can grab lunch at one of the vendors indoors and then shop around. It's fun to get to know the owners of each booth and to find out the best place to get what. This way you're supporting local in the purist way too.
If you live and Cleveland and you haven't been, go now! It's addicting. I only wish it was easier to get to on the bus from the east side of Cleveland.
Protip: Come right before closing to get some great deals on older produce. It's not the most fresh, but I couldn't argue with three pints of raspberries for a dollar!