Sunrise 516-593-1600 - be aware that you are in NY and you get what you pay for. The good news is the Sunrise is $67 a night if you are crew ($85 normally). This place ain't the Hilton and it ain't even Motel Six. Picture a 1960's - 70's version of a Holiday Inn that never made it through any more decades of time. Just stuck in a time warp. The hotel is about 7 miles east of the airport and have great van service but you are heading out of the city.
Best Western JFK is second choice - sorry don't have their phone number because it was hard to get rooms there. Good van service - crew breakfast and dinner menus - you have to ask but it is a bargain on their normal prices.
Ramada - don't plan on buying food in there. wow is it expensive.
But the hotel is nice.
You may want to consider a hotel out in Rockaway or Far Rockaway, out on the breakwater on the Atlantic. The neighborhoods there are kind of spotty, but they're better then the ones north of the airport, and you'll still be close to the airport. Try to stay away from Ozone Park, north of JFK. The 'hood is kind of nasty- you'll definitely want to be back in your room by sundown!
Just a note on the best western: I had an overnight in JFK last week and stayed at the Radison because it appears the Best Western was closed for remodeling? I once did 3 months TDY out of Kennedy and have come to the conclusion that there all pretty expensive and there is nothing to do close by.( sorry)
Pan American on Queens Blvd. they will pick you up at JFK or LGA. Close to the sub for going downtown and the Sage Diner next door will give you more bang for your buck then you will get anywhere. Most commuting DAL FA's and flight crews stay there.