I want to see the Statue of Liberty eventually. 

I would say, Jim, that you should also set a little time aside to visit a museum, as New York is pretty much second to nowhere else on Earth when it comes to it. The Whitney (as I mentioned upthread) is great, and its position right at the end of the High Line park (which you really oughta check out) is convenient. Whitney is pretty slim, though, and its benefit usually lies in what exhibits they have up - the Edward Hopper one from a couple of years back was fucking awesome, for example, and the Biennial (when it's on) is at least pretty interesting.

But, seriously: the Met, MOMA, Frick, Guggenheim, etc. Any one of those is a cultural landmark for a reason. And the 'secondary' museums are also all worth consideration: the Cloisters, the Society of Illustrators, any number of cultural specific ones.  And of course Natural History/Hayden.

KEENES steakhouse is over 100 years old and is worth a visit for a good steak if that's your thing.

EDITED TO ADD: St. Mark’s moved way out in Brooklyn and I haven’t been to the new location, so I can’t speak to it being worth a trip.

Our first night there were seeing Moulin Rouge (not my choice, but, hey…) at the Hirschfeld Theatre. Very close by is the Playwright Celtic pub I may have to duck into.

The next day we’re planning on the Statue of a liberty / Ellis Island, 9/11 memorial, maybe Empire State. After that…

JB, Evolution is definitely on the list.

Dave Kopperman: we are doing the High Line at some point, and I want to see every museum you mentioned; but, and I want to be diplomatic, my wife is not a museum person. We once saw three Smithsonian museums in a single afternoon. So I might get lucky enough to see the Natural History museum, because it was in the Night at the Museum films. 

All great suggestions.  In December, we did a walking food and history tour of Little Italy. The guide was fabulous and the food samples were outstanding.  The NY Public Library (free) is in the middle of everywhere and the Polonsky Exhibition has some gems. The original Winnie the Pooh animals, Washington’s Final Address, a Gutenberg bible, a copy of the Declaration of Independence, and more. 

The Seinfeld Diner- Tom's Restaurant- is at 112th and Broadway.  Columbia's main gates are at 116th and Broadway and I have to say that Koronet Pizza at 111th and Broadway is a favorite.  

And Riverside Drive is beautiful for a stroll.  

Also, back down in Hell's Kitchen is the Irish bar Scallwags on Ninth Avenue and Kathleen and Rose are great bartenders.