It depends so much on location and the condition and size of the apartment (we don t say flat here in the U.S.)The cheapest you could probably find would be about $1,500 a month, and that would be for a tiny place wayyyyyy out in an outer borough. But you could try renting with a roommate, and that might help save on costs. It might, at least, get you closer to Manhattan.
In manhattan about $2500 a month, in Queens about $1000 a month, both for a one-bedroom apartment in a relatively safe neighborhoods. Nonetheless most buy co-ops.
I can help find you place a good place for around 1100 in Manhattan. Im a realtor here in the city. Feel free to contact me if you are interested in moving here.Maggie FinleyMetropolitan Property GroupMove2Manhattan@yahoo.com