The West Side Market is a Cleveland institution. Still an open air market after all these years. The building is covered, but open on the sides (and there is one enclosed section now, but who's counting). Why anyone shops at a regular supermarket when the West Side is just a short drive away is beyond me.
Fresh, fresh, fresh - those are the three words to remember. You walk from stall to stall and buy what you need from each vendor. And these vendors know their products (some have been selling at the Market for generations) - ask questions! Most vendors offer samples too.
Any food item you can think of is probably at the West Side Market: fresh Ohio produce, meats, poultry, fish, divine cheeses, bakery products. In short, anything you can get a the supermarket, but without the supermarket price tags.
Oh, did I forget to mention - the prices are awesome. You won't believe what you get for the money.