The greatest city in the world...Boston, MA!!! Although your rent restriction will have you living on the fringes of the MBTA.
It will have him living in a high-crime area that's nowhere
near the MBTA.
If he wanted to move to New England, I can add that in general rent is more expensive in Mass (and
forget about living with easy access to Boston on that kind of money without a fuckton of roommates), but benefits are generally better and more easily accessible (health care, government money, etc). Rhode island (Providence, prolly, if he wanted to not need a car), everything's cheaper, but he wouldn't probably be able to afford health insurance. Catch-22.
Ultimately it might be more cost-efficient to buy a bloody car and live someplace that's sustainably cheaper.
When you decide to where you want to move, you should checkout the public welfare system for that county. Welfare is responsible for HUD and Section 8 housing, and they will help you. I am 100% sure you qualify, but sometimes such programs take a few months to get enrolled in. I suggest that after you figure out where you want to go, apply for these programs in the appropriate county.
Also, you can check craigslist and maybe get a roommate to share costs with ? It's an idea.
Try
years, and more than a few, unless you're a single mother or a veteran. Or maybe a bit quicker if, again, you're willing to move to an uber-high-crime location (ex. the projects).
Stultus, if you find anyplace that meets half your specs, even let me know; I'll move in next door.