Jamaica Queens - City is investing allot of money and they just rezoned to R7 and some hotels and popping up on Hillside Aveue as well as condo development.
Bed Stuy, Brooklyn - Was getting very strong over the last few years. Allot of out of state transplants look here when they are price out of manhattan. The only problem is will they keep coming to Bed Stuy if Manhattan gets more affordable?
Bronx - Im not sure this but if you are from the bronx, the South Bronx seems like it might be making a move.
Have you narrowed down any "up and coming" neighborhoods as of yet? I've been helping someone search for a multi family residence with that same request...however I'd love to know the specifics of yours...feel free to get in touch at email@example.com