In Brooklyn you can usually find a studio/1BR between $1000-$1500/mo, depending on neighborhood.
Greenpoint/Williamsburg is probably ideal for a mix of affordability and livelyhood/shit to do in the neighborhood; you'll have to take some time to find a good price for an apartment though.
DUMBO has a pretty big startup hub, but it's pretty expensive, so it's not an ideal place if you're bootstrapping.
Honestly, you can probably move to anywhere in the 5 boroughs thats within an hour of midtown/downtown and it would be the same in terms of tech activity, meetups, etc., and that covers about 80% of NYC.
I would personally recommend a quiet residential neighborhood like Bay Ridge in Brooklyn; it has great food, decent accessibility by train/bus, and affordable rent.
Feel free to hit me up if you're in town!