Every place, no matter how liberal, has its conservative outposts. (And vice versa.)
There are conservative parts of Manhattan. There are parts of the island that voted for Romney. (Yes, really.) But by no means is New York City conservative. Quite a few of the first responders who died on 9/11 and those construction workers who worked to rebuild the city with American flag patches on their helmets came from State Island or the more working class parts of Brooklyn.
Meanwhile, on 9/11, while evacuating the area, I passed anti-war protests in progress. (Yes, while the towers were burning. There were anti-war protests. Feel free to take a breather for some cursing. I won't mind.) In some ways that's worse than the Muslims in New Jersey celebrating on 9/11. These were Americans. Not Pakistanis. But NYU college kids for the most part.
Some New Yorkers pulled together on 9/11 and afterward. And some stabbed us in the back.
What are New York values? Who the hell knows. Most of the city's identity lay in its white working class which is vanishing. What remains is generic minority Dem rule government of the kind you can get in any major city.
New York values today are Starbucks, Whole Foods and a $3K a month apartment adjacent to them populated by two roommates from California who are in banking.
I still like New York City, but I don't kid myself about it. Even the city that was on 9/11 is hardly here anymore. The FDNY and NYPD have been PC'd as much as possible. Your next FDNY firefighter will probably be an affirmative action hire who can't physically save you and wouldn't bother anyway.
Manhattan still has conservative intellectuals. And Trump named Buckley for a door prize. But William F. Buckley spent more time attacking New York City than Ted Cruz ever did.
It was after all Buckley who wrote, "You can’t walk from one end of New York to the other without a good chance of losing your wallet, your maidenhead, or your life". But New Yorkers like to talk that way.