I know you think all you can afford is a studio or 1BR, but I highly recommend looking at multifamily properties, especially if you're planning to rent it out in the future.
Multifamily properties only require 3.5% down for FHA loans, and the rental income generated by the units you're not living in offsets the qualifications you need to get the loan. They also generate far more rental income. A single-unit co-op or condo will likely barely break even after costs (in the best case) when you go to rent it out, and the wear and tear on the apartment are very likely to pull you into the red overall in the long term.
I'd let the multi-family hunt take me further east into Crown Heights as far as Kingston Ave. I would NOT go further east than that. I'd also look in Crown Heights South, especially in the Franklin/Bedford/Rogers areas. Here you have the same great proximity to the 2/3/4/5/S trains as well as all of the new businesses and restaurants on Franklin Ave, but the prices haven't quite crept up there at the same rate.
Three-family house. The 9-beds is probably a stretch, but the rentals here can easily command $1800-2200 depending on the condition. You put down 3.5% -- $21k -- and you'll need another $20k for closing. Including PMI and taxes, your monthly payment will be somewhere south of $4000. Now you're right on the verge of having your housing covered by your tenants, if not over it. And you've put down less money than you would need to buy a $300,000 condo with 10% down. And you own land. You have a back yard. Your doggy is happy.
Now, that particular house has been on the market for some time. I haven't seen it, but I'm guessing there's probably a reason for it. It's just an example, and even if a house needs work, there are ways around that, such as an FHA 203k loan, where the bank gives you the money to pay off the buyer as well as a sum towards renovation.
I'm not a broker, banker or a contractor, just someone who was in the same position as you -- long-time Manhattan resident shopping for a condo -- when I stumbled upon the possibility of doing something that I didn't imagine was possible. I also happen to be someone who has owned a single-unit condo in the past and rented it out, and I can tell you that's NOT something I will ever do again -- the margins are far too low to justify the risk.