Corky & Lenny's is an Eastern Cleveland institution, credibly "New York style," while at the same time being "Cleveland style." Tomato and lettuce on a corned beef sandwich might loose some style-points in Manhattan, but at C&L's it's simply part of the experience. Their sandwiches are very large (not huge), contain a good quality of meat and are, at $9-11, fairly priced. Most offer cheese as either part of the sandwich combo or as an option; another localism.
Authentic to the style, C&L's offers deli-style smoked fish, and their smoked whitefish is often what drew me here (or to the now-defunct Cedar Rd. location) during my college years. Their chicken in a pot is decent, as well.
Service has that true-to-form grumpy exterior/soft heart which has become an icon of New York delis. Make the effort to connect in a genuine way and you'll find warmth and personality.