Taxi from JFK to your hotel is $50+tip for all three of you "door-to-door", much easier than schlepping your bags on a train or bus. If you want to schlep and save some $ take the subway; Airtrain to Jamaica station to E subway to 5th Ave./53rd St. Walk one block to 52nd St., hotel is between 5th and Madison Aves.
Taxi from JFK to your hotel