Definitely book a car. Most car services operate to Connecticut. It wont be cheap.

Having said that, how long are you going to be in Greenwich for. There is only one decent hotel (the Delamar) which is normally fully booked. Make sure you have a tentative booking there first before arranging flights even. Any other hotels would mean a taxi ride. Also will you have much spare time in the evenings. Greenwich is really dead. A few posh restaurants (one of the two most expensive neighbourhoods in the US) and thats it. Stamford is the alternative and that is a bit soulless.

I prefer to stay in a hotel near Grand Central and take an hour's train there and back everyday to enjoy the bright lights of New York in the evenings.