@wm02 could correct me. Not from the city but have tons of friends and random associations with people from the city. Spent a decent amount of time there.
You are spot on, usually Jets/Mets, Yankees/Giants. The Jets/mets contingent is largely Long Island and some specific New Jersey suburbs.
Giants/Yankees like every other borough and suburb. Most of the state until you hit Albany. Binghamton mostly Giants. Syracuse is where you get like 50/50 Giants/Bills with some Jets, Cleveland, Pittsburgh peppered in.
No self respecting New Yorker likes the Nets. They can move to Brooklynn, have the Jay-Z ties, but it's a New Jersey team. My dad is a knicks fan from Western New York. I root for the Knicks, but always been Lakers through and through. The Knicks have been such a trainwreck since the 90s so it sucks.
But Knicks are the only team Jets/Giants fans all usually pull for. I also find the breakdown of who roots for who interesting because there really isn't an actual tangible thing that makes people pull for whoever. It's usually just passed on through family.
But yea, screw the Nets. Wish they'd go back to Jersey.
Jets also usually align with Islanders, and Giants the Rangers.
Also, old timers who liked the baseball giants usually fell into the Mets camp.