I'll have a 5 hour layover in the JFK airport and I'll be suffering from jetlag. Is there a cheap capsule hotel where I can pay for, say, 3 hour stay and have a short nap?
To the best of my knowledge, this page lists all the airports with sleeping pods inside the airport and JFK is not listed. Minute Suites indicates Chicago O'Hare is coming but I can't find any company even planning to open a capsule hotel inside JFK much less having one right now. As the page above was last updated 15 December 2015 they are missing JetBlue's JetNap which are indeed at JFK but they are only for twenty minutes which is close to useless and many reviews complain about questionable cleanliness.
If you want to go outside of the airport, obviously the question is too broad, it's practically impossible to even count the options to grab a quick shut eye around an airport the size of JFK.