Cleveland's West Side Market
There are a lot of great things to take home with you. I have been living in Dayton about a year now, but used to like to go to Ohio City Pasta & to a stand that sold pierogies of all sorts. There was a good spice store near the front entrance. I also used to get Cornish pasties from a stand near the back, on the restaurant side.
Maha's Falafil (their spelling).
Volio Costa Rican coffee - at the end of the shorter section of the produce arcade - free samples :)
Also nearby the market-- if you are a beer drinker-- McNulty's Bier Markt is across the street and has a ton of (bottled) Belgian beers-- fun to sit outside and try a beer sampler. If you are a home cook, Penzey's Spices is right across the street.
Dohar's Smokies. Crepes from the crepe stand. Maha's Falafel. Ohio City Pasta. Corn tortillas from Orale (and their prepared foods are delish also). Bread from Mediterra. Cambodian treats from Kim Se. Fudge from Ohh Fudge (or brittles - if you like spice, try the Habenero). Unusual quinoas, cous cous and similar items from Urban Herbs.