I might be able to help you out but you will have to open your options to other parts of the city due to you budget.
This is a tricky question, especially as to start off with I think a 3 bedroom in Gramercy would go for more than that! What country is she coming from? It might be possible to arrange for letters of credit from her country of origin and or possibly have her employer co-sign. I agree with Eileen that her best bet is to offer 6 months to a year in advance perhaps in escrow (please check with an attorney) I do know of a 2 bedroom with loft spaces in each room on the UWS that is in that range.( the current tenant was in a similar situation)
Let me know if you'd like me to find out if it is still available. Good luck!