If you are truly, honestly only looking for a bed then look at The Jane: »
www.thejanenyc.com/ I've stayed there a few times and I'm pretty happy with it when I'm in the city by myself and only need a room to sleep in.
Be forewarned though: while it's a good, clean hotel in a good area the rooms are
TINY and basic and restrooms are shared. I'm being completely serious when I say that if you lay a roller bag flat on the floor you will take up about 1/3 to half of your available floor space that isn't your bed.
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JFK is a better choice, and if the OP is interested in going outside NYC to stay, they could take the Airtrain to Long Island too..
Or they can take the Airtrain from JFK to Jamaica and either take the LIRR to Penn Station, or the subway into Manhattan, Queens or Brooklyn.
Airtrain Newark to Newark airport station then NJ Transit rail into Penn Station really isn't any different.