As themicah suggests, you should make sure the rental you want falls under the free rental you have. If you can, rent near the Holland Tunnel and then take US 1 to the airport.

It is hard to advise on what hotel you should take without understanding your situation, but I don't see how you would end up in Staten Island or Carlstadt. Stay in Manhattan if you want the extra night in Manhattan, or near EWR if you just want to wake up, return the car, and go.

Make sure you understand how the suspension of the EWR AirTrain (slated to last through July 15) affects your plans.