new york city

I would not fly in and out of Syracuse. I would do a multi-city ticket. Fly into Syracuse, take the train to Penn Station, and then fly out of NYC. Penn Station is good for getting anywhere. You will then be in Manhattan and be able to get a hotel there. Most of the tourist objectives for NYC are in Manhattan. You can then take the subway or bus between the different sites easily. Getting to the airport is best done by shuttle or taxi.