When it comes to Cleveland cuisine, Melt is the best. You will wait for about an hour (usually more) at just about any time of the day or night. That's the one complaint I've ever heard about Melt, they're too busy.
They have a HUGE beer list. Their food is creative and delicious. The Parmaggedon is a pierogie sandwich and the Big Popper is basically a giant jalapeno popper on bread that gets beer battered and deep fried. Delicious.
Melt is also vegetarian and vegan friendly. The soda does tend to be a little flat due to old carbonation lines (I asked once) so I stick to water, tea, or lemonade. There are over 100 kind of beer if that's more your thing though.