For me, a pub is a location where I want to go hang out for an extended time with friends. Ideally, it should be local and neighborhood oriented, but my favorite is not strictly local to me. Primary beverage should be beer, but cider and whisk(e)y are also cool. There should be a simple food menu (as in relatively few items compared to a restaurant).
There used to be a great Irish Pub called O'Flaherty's in the French Quarter in New Orleans, but it's been closed for years. Pretty stereotypical example with beer, darts, and billiards with a lot of dark wood and leather couches.
My favorite Pub currently is the Avenue Pub in New Orleans. It's always on my list of first recommendations for beer tourists. Great beer selection along with whisk(e)y and a knowledgeable staff. Food is a contrast of simple and high-end (burgers and dump truck fries are the standard items, but done with a local farm-to-table ethic).