Since boats don't always dock on time, there's no way to truly calculate how much time you'll have in the Wormy Apple. Then again, you are vague with saying that the disembarking time is 'early'. Are you saying 6 in the a.m. or 2 in the a.m. or perhaps later? Additionally, where will the ship be coming in?
The passenger ship terminal is in the west 5os over by around 12th Avenue. From there you could likely trek over to Central Park and then take a quick walk down B'way into Times Square. Then hop on the bus...no, scratch that, it takes forever...then walk east to Grand Central and go on in. They redid the ceiling in there a few years back so the constellations are back to looking, well, er, um, stellar.
From there, it's a short walk down to 34th Street and the Empire State building, although to save a few moments of time, I'd recommend taking a trip up to the Observation deck of the simply fantastic and fabulous Chrysler Building which is right there by Grand Central.
From there you can head further east and at the very least, view the United Nations building. Not sure what their visiting/touring schedule might be.
It's impossible to really say what the best things are for visiting, and given the time constraints, I'd have to add in you need to factor in waiting times at certain locales. The thing is, so much of my life has been attached to the city that I rarely notice or fully comprehend how all the things around me are great tourist venues. That, by the way, is the answer as to best places. Honestly, any place is something which will be on somebody's 'best' list.
As far as transportation, it depends on your abilities. Are you a good walker? If that's the case, then walk. Other than that, subways are quick; however, you'll need to know the routes in advance to get from point A to point E or point J. Taking a bus in New York can be infuriating and often times you will notice people walking along faster than the bus. If the President is in town, you can add to the snail pace as traffic is prohibited in certain corridors and rerouted like mad. Cabs are good, but mighty costly. They are also harder to get if it's raining. Are you good as a bicyclist? Maybe rent a bike to maneuver around town.
Towards the end of your day, you can get an expensive cab or car service to LaGuardia, or hop on a bus to get there or use the public transit, and take a train, then transfer (free) to the M60 bus at Astoria (need to take the R or N train from Manhattan). I know other trains have bus transfer spots as well, check the mta.info website to learn more.
Remember, you need to arrive at the airport at least an hour in advance.
Have a nice cruise, and visit and be sure to keep us up to date as time permits.