Dave's Cosmic Subs is an iconic restaurant in downtown Chagrin Falls and they serve the best sub sandwiches in the Cleveland area as far as I'm concerned. The bread is fresh baked, the ingredients are tasty and of high quality, and the pickles are to die for (just don't ask for extras or where Dave's buys them, it's a 'secret').
My only complaints would be that they do not accept credit cards and that the line can be a bit long. Oh, and Dave himself isn't exactly the most pleasant bloke in the world, but he's never thrown me out or given me trouble. Just feign interest in his hair-metal band and/or be an attractive female and you'll do just fine with Dave.