What makes a good deli is a place that, one, is generally family-owned or owned by individuals that care. Delis that are owned by large corporations tend not to have that same soul. And two, delis that make as much of their food from scratch as possible.
Detroit is a great deli city. If only GM could learn from what the delis in Detroit are doing! The best rye bread anywhere - double-baked, crispy, warm rye that they serve their sandwiches with - and great corned beef. It's a passionate deli town.
A Jewish deli should specialize in, first and foremost, Yiddish foods, the foods of the Eastern European Ashkenazi Jews. So, if it's a place that specializes in pizza or chicken wings or diner food and then does a corned beef sandwich on the side, it's not a Jewish delicatessen.