You can't say you've seen NYC until you've seen it from a boat. Hop on the ferry from anywhere to anywhere and you'll see what I mean. Not only will you see excellent old buildings and factories--the inner workings of the old industrial city--but you'll head out under working bridges and see the skyscrapers in all their towering glory. And once you've done it, do it again, at night.
Roll N Roaster is a fast food place in Sheepshead Bay that has been open since 1971. Get the roast beef sandwich with cheese and a bottle of Moet champagne (not joking).
City Island is a seaside town in the Bronx. Known for its fishing, seafood, and main street it is a self-contained working-class haven. The buildings range from late 1800's houses to 1960's storefronts, and you can smell the ocean everywhere on the island. Restaurants and local pubs dot City Island Ave, and even the few empty storefronts stay vibrant.
I love having Breakfast at Le Coucou - you'll find me here several times a week. Le Californien, OJ and Expresso! Dinner is very formal - but amazing if you dig the French high-end, but Pro tip: They have amazing drinks, so drop by and hang in the bar for a few drinks!