Just visited NYC in the winter about a year or so ago. Here's what we (a couple like yourself) did and what I thought about them. We did pretty much all touristy stuff, but we just wanted to see as much as we could while we were there. You can fit a lot in in a short amount of time.
Empire State - Def gotta do. Go in late afternoon and stay for the sunset. Cool to see the view in both daylight and night....especially night.
Sightseeing tour (red busses where you can sit on top...can't remember name) - Good thing to do like the first day so you can see almost everything and get a good feel for the lay of the land. You can get on and off all day...thought it was totally worth it. Takes you by almost everything you want to see in Manhattan.
Ferry to Statue of Liberty - pretty cool, but if it's cold and/or windy, you better dress WARM. It was like low 40s when we were there and somewhat breezy and let me tell you it was frackin freezing. We were bundled up, but I can't imagine doing it if it were legitimately cold. Didn't visit island...just rode by it.
Broadway Show - I wasn't too hyped up about this, but it was actually really good and worth it. We didn't have a specific show we wanted to see, so we went to TKTS the day of and got really cheap tickets for that night. Fairly long line, but worth it for the savings. TKTS is in Times Square I believe. Look it up.
Times Square - cool to just see at night...obviously
Central Park - definitely walk through it - we ice skated there and it was ok...probably too pricey for what you got and very crowded pond. Trump has a f'n cash cow with that thing.
Rockefeller Center, Ground Zero, Wall Street, Letterman Studio, other touristy things - cool to see, but that's about it. Don't take much time.
Little Italy and Chinatown - I recommend visiting this and eating in Little Italy. We just picked a place based on a travel guide review.
Travel in and around city - take the subway and not cabs. cabs way too pricey. you can actually take the subway & train from jfk all the way to manhattan, however it takes fairly long (I think like an hour). Kind of fun to ride it through Brooklyn and some neighborhoods. Fairly uncomfortable having luggage with you on a very crowded subway/train with a bunch of working class and diverse NYC people though...just fyi. We did it w/no problems though. Did this to save large cab fare.
Modern Museum of Art - maybe if you're into that kind of thing it would be cool....i thought it was only ok. some cool things, but mostly i was kind of tired of walking around.
I think that's about it. It was a fun trip. I was told to walk across the Brooklyn Bridge into Manhattan too...though we didn't do it. I don't really remember everywhere we ate and drank, etc. The places we went were good, (Get a hot dog from a vendor and also get a bagel from a hole in the wall place) but we are kind of like clams with regards to food stuff when traveling.
My last piece of advice is to take plenty of $$$$$. That place will just suck the cash right of you.
