Have a drink at Benelmans.
Get a coffee in Cobble Hill. Or get another drink at Clover Club. Or both.
The Met for a minimum of an afternoon.
In October, go to a Rangers game. Or if, god willing, the Yankees make the postseason, find a decent sports bar and watch the fun. (Or get tix. Nothing like playoff baseball in NYC.)
Literally any cuisine you want at nearly any price point. I have tons of favorites but find your own. Currently still loving Frenchette and Sofreh.
If you're there in late October, La Bohème at the Met (opera not art).
Strand Bookstore.
Shopping on Mercer Street (If you're youngish), Bergdorfs (RIP Bender's), or Bedford Ave in Williamsburg (If you must).
Leaf peeping in Central Park.
Agree with Staten Island Ferry.
I can't do the 9/11 museum, fwiw. Too soon. But the Tenement Museum is amazing.
Moma, the Frick, and the Whitney. Also I love the Cloisters, though they're not the easiest to get to.
Jazz at the Top of the Standard for the views alone.
But those are just some of my favorite things. You could spend a lifetime and just scratch the surface. If it helps: what kind of vacation do you want? What do you like to do, in general?