There's a list published somewhere but this is what I know:
Ramada Inn JFK $44-49 nite. They totally cater to air crews.
Ramada East is quieter, nothing around to do. Same price.
Country Inn/Comfort Inn JFK 59/nite
Red roof JFK Is cheapest, but it's sleazy!
Baymont is a Mesa hotel. Offer to pay cash, and they give you a great rate. However, there is nothing around that hotel.