While in NYC I had the chance to take the GrayLine New York Double Decker Bus. We took the hop on, hop off tour downtown NYC. We were able to get on and off at various stops like the World Trade Center memorial, Empire State Building, Statue of Liberty, Brooklyn Bridge and Central Park. The first couple of tour guides we had on the bus were great, they explained what buildings we were seeing, how old they were and some history behind them. It really gave you an idea of just how neat of a city NYC is. They were also able to give suggestions as to what you would want to get off and see at each stop, a place to eat perhaps or a store you might want to stop in.
I was glad for the advice they gave on getting tickets for the memorial, we were able to get started in the right direction. I also took the oppurtunity to go walk the Brooklyn bridge and the tour guide was informative as to where to go for that. I would definitely recommend doing the hop on and hop off tour-it also connects at the start of the Brooklyn tour, so you could buy both and get the best of both worlds. I would suggest bringing a few $1 to tip the tour guides as you get on and off.
That hop on and off tour would be great for your first day in the city, you get a feel for where everything is, you can pick what you want to spend longer doing, you can get on when you want and off when you want. The lines were not that long and the busses came every 15 minutes for almost the entire day.