JFK airport has the Hilton Garden Inn on 134th St, and the Radisson on 140th ST. Both hotels are in an area Jamaica, NY. Neither has transfers to the pier only to the airport.
LGA has the Marriott on Ditmars Rd, and the Pan American hotel on Queens Blvd. Both are in an area of Elmhurst, NY.
All the hotels provide atleast 1week parking.