Flushing Motel (34-50 Linden Pl, Queens) has that certain hourly-rate ambiance to it with the mirrored walls and sketchy location. But it seems like it's primarily for nooners. For overnight, it gets almost as expensive as better hotels.
Jets Motor Inn (139-06 Queens Blvd, Queens) screams cheap motel/likely to stay next to meth tweakers. Dumpy furniture, old bath fixtures, hot & cold running roaches.
JFK Inn is right near the airport. Looks super sketchy and sleazy. Really dated, shitty housekeeping.
I'd have recommended the Hotel Carter off Times Square if that was still open and you didn't mind a super sleazy hotel complete with bed bugs. They finally closed that eyesore.
I know your request was serious and I was trying not to joke with this -- you aren't looking to stay at The Plaza -- so I went for the cheapest properties that didn't have a lot going for them. Someone could have a lot of fun trying to find the worst hotels in NYC, for years the Hotel Carter was it and had no equal. People actually got murdered there and it was a haven for crime.
Good luck, come back safe.