Hi, I did 3 days in NYC last yr as a first as well and if you want to maximise sightseeing i would recommend getting the New York Pass from planet hollywood. It has a map showing where everything is and gets access to a lot of attractions. I managed to squeeze a ridiculous amount in by coming up with an itinerary (museum of modern art, met, planetarium, guggenheim, 3 river cruise, intrepid + lots more).
Staying near Rockefeller Centre make sure you do top of the rock (central park, empire state and chrysler building views). I enjoyed this more than empire state building and it took 15 mins to get to top, compare to 2 hrs 45 mins for empire state. almost 7 years ago
New York is great for walking around, but dont forget to use the bus and subway system too. On my very first visit I did one of those hop-on/hop-off bus tours, not because I particularly like them, but it did give me a great overview of the city and allowed me to then focus my remaining time on the areas that I really wanted to go and see.
I would usually split my day up - so early morning coffee on the way to a museum where I stayed until lunch. An early lunch followed by hitting an area such as Chinatown, TriBeca or Greenwich Village. I normally picked one thing I really wanted to do/see in that area and then gave the rest of the time for just walking around and exploring.
I used a mix of google search, Lonely Planet and one of those Top 10 books which helped me to target where I wanted to go and what I wanted to see.
The museums I love are:
MoMo (or for more cutting edge then P.S.1)
Tenement Museum (and then go to Katz's)
Places/things to see:
Statue of Liberty from the Staten Island ferry
Grand Central Station/Terminal
Grimaldis Pizzeria, Brooklyn
Katz's Deli but this is a bit twee and there are other fine places offering pastrami etc
McSorleys Ale House
Blue Note Jazz Bar
Nathans almost 7 years ago