When we went we walked everywhere ~ miles! we were advised to do this, and I am glad we did as we took in all the sights and smells of Manhattan ;o)
There is no Central Perk, I'm afraid..not that I saw one, anyway! you can get a taxi outside the airport ~ there are always yellow cabs outside Newark airport (it'a an experience to survive, I have to say) there is a toll to pay, which the driver will ask you for.
Central Park is wonderful (and clean) in fact the whole place is very clean. Made London look even more filthy than it probably is. It was great to see it all ~ Statue of Liberty, Empire State Building and the Dakota Building (the apartment building where John Lennon lived and died).
We actually hadn't planned to visit Ground Zero ~ we just stumbled uopn it while walking, believe it or not. It was the day before the anniversary and to be honest I wasn't prepared for the grief I felt. The place is very quiet, despite being in one of the busiest parts (financial district). We visited the church opposite and lit candles.
There were leaflets in the hotel listing excursions. There is a 'Friends' tour but I have left that for another time ;o)
You will have a fantastic time. Just remember to take plenty of of money (especially for tips!) and enjoy...