Thought this was a good deal.
Flying to New York JFK from London Gatwick with Norwegian - Dates start around 10 Jan 15 and end around 8 Feb (before it gets costly) Flights are direct.
Flights work out £331 each (For example Jan 17 to Jan 20th) (without a bag/food/seat selection) but can be bought in a deal for £70 return - You shouldnt need a bag for 3 days though and you can buy food in the airport/on the airline during the flight.
Hotel - Hotel Newton on Broadway (via booking.com) works out £157 for 3 nights. The Subway is literally right outside the door and has the express 1 line on it (15 mins to times square) This hotel receives a 4/5 on Tripadvisor.
The room is a double with shared bath (Not that much more to upgrade to private bath)
I have stayed here before and would definitely recommend it.