Often when I rent a car, I don't include my flight itinerary so I am amazed that you are asked for it. Are you sure about that?

Renting a vehicle in Manhattan is expensive. It will be even more on a one-way rental. I think you're best bet is renting at EWR. Look at the various rental car fora here in FT and search for discount codes and coupons to be used for online reservations on a weekly rental. You are sure to find a decent deal for that time of the year.

It is easy to get to EWR. You can take a bus or train; you don't need to spend lots of money on a taxi. If you have a lot of luggage, the Supershuttle can pick you up at your hotel and take you there. I don't recommend it if you are under pressure to catch a plane but for you to rent a car, it should be fine.