I ran into a German photographer at Inwood Park a couple of months ago who was staying at the Five Towns Inn on Rockaway Blvd near JFK
From the outside this place looks a bit dodgy but he said the rooms were fine. He said you could see some of the 31R action from the room, but in-room photography is probably not an option. More importantly, however, if you don't have a car you should be able to walk up to the Firestone lot, a popular photography location for 31R arrivals at JFK
. If the 22L approach is in use as it often is, you'll have more difficulty, as the common photography spots for that runway are several miles away. And as Art noted, for 13L the Ramada is your best best, but you'll need to venture out a bit for decent photos.
I've used Art's spotting web site frequently and recommend it (in fact used it this morning to get Tampa info - thanks, Art!).