I can say that the cheapest neighborhoods are Brownsville and East New York and East Flatbush but even these areas have rents that have increased. Usually you'll find basement apartments, small regular apartments or one's not in very good shape at those prices.
But if you look hard enough you may find a diamond in a pile of hay. Good luck!
Sheepshead Bay, Gravesend, Bath Beach, Bensonhust, Canarsie, Flatbus, East Flkatbus and Midwood just to name a few.
REMAX NEW YORK
261 4th Avenuue, Brooklyn NY 11215