AlHal

Email students from both programs. I'm a former Fulbrighter and I field emails all the time from people in just this sort of situation. Only people on the ground really know what each program is like and what you're actually going to be able to get out of it. Tell them your plans and ask them their advice.
And stop it with the, "which is more prestigious" B.S., take the option that fits your interests best and excites you most because that's the one that will help propel you forward. 

Also, DON'T TAKE THE 86. My colleague takes it to Harvard Sq from Cleveland Circle, and it frequently takes over an hour during rush hour. 
 
Don't do it.

You can still find something in Brookline if you're flexible. You can take the T's Green C line from further out on the Brookline/Brighton border (Washington Sq and further) where things get a little (not tons, but a little) cheaper. Steer clear of the B line, if you're not comfortable with billions of drunk undergrads running amok and puking on your front steps, this is a good warning to anyone. Really steer clear of the B-line in general. It will make you want to stab yourself in the eyeball, some stops are less than 1/4 mile apart and they have to stop at every light. It's a disaster. The C and D lines will bring you to Kenmore Sq, which will then be easy for you to navigate wherever you need to go on BU's vast "campus."
 
If you're really set on your own place, you may have to put up with a "garden level" studio if you want to keep the price under about $1300. You'll sacrifice daylight, but you'll also be a student, so... who needs sun?
 
Your other option for BU would be to look at Brighton Center around the St. Elizabeth's medical center, and on the 57 bus. It is a dream of a bus, it goes so quickly, often passing the dreaded B-line when it meets up with Commonwealth Ave.

You can still find something in Brookline if you're flexible. You can take the T's Green C line from further out on the Brookline/Brighton border (Washington Sq and further) where things get a little (not tons, but a little) cheaper. Steer clear of the B line, if you're not comfortable with billions of drunk undergrads running amok and puking on your front steps, this is a good warning to anyone. Really steer clear of the B-line in general. It will make you want to stab yourself in the eyeball, some stops are less than 1/4 mile apart and they have to stop at every light. It's a disaster. The C and D lines will bring you to Kenmore Sq, which will then be easy for you to navigate wherever you need to go on BU's vast "campus."
 
If you're really set on your own place, you may have to put up with a "garden level" studio if you want to keep the price under about $1300. You'll sacrifice daylight, but you'll also be a student, so... who needs sun?
 
Your other option for BU would be to look at Brighton Center around the St. Elizabeth's medical center, and on the 57 bus. It is a dream of a bus, it goes so quickly, often passing the dreaded B-line when it meets up with Commonwealth Ave.

If you're really committed to living on your own, I would try to look around the Allston/Brighton area, JP, or Somerville for a studio around or less than $1,000 (although, don't expect to find a large inventory). Also note that if you go through realtors they may tack on an additional month's rent as a 'realtor fee'. If you don't mind living with roommates, I'd suggest looking for rooms available in apartments on craigslist- this often prevents you from having to pay a realtor fee, and if the roommates there have already lived there a year, chances are the apartment is already pretty well stocked, a serious bonus if you're moving from somewhere far away! Right now I live in a 4 bed in Brighton for $730 with heat and hot water included and a 2-minute walk to the t. It's hit or miss rather buildings will include heat in the cost of rent, but if you can find it, it is definitely worth it (as someone mentioned, a lot of the buildings are old and poorly isolated, old apartments of mine have had heating bills of up to $300 a month) The good thing about having roommates in Boston is that many young people here are very academically minded- either in school, trying to get into school, working research jobs, etc, so in a way, a lot of us are coming from the same place!

just an FYI to everyone thinking about moving this fall: in the student-heavy areas, a lot of people re-sign their september leases (or notify their property managers that they won't be doing so) in march-april, so keep an eye out!

ALL TRUE
also, I commute from JP to Cambridge & it typically takes an hour

I want to be clear, my apartment is a freaking unicorn. Don't expect to find a studio anywhere outside of Allston or JP for under at least $1100 (which I would still consider a great deal.) I scoured the internet for months and pounced when I found it.
Finding much outside of Sept 1 will be hard. Consider coming to Boston, taking a sublet for a summer, and learning about the city. You'll be on site in the freak case where you find something as cheap as my place, but you'll also get a better idea of what you're able to find/afford. 
The realtor's fee is something that CAN be avoided, just do a search on craigslist that excludes realtors. It means your choices will shrink substantially, but they're horrible and nightmarish 20-somethings working solely on commission and they will make you hate life. I suggest not using them, not just to save money, but to save your sanity.
Don't live in JP if you're planning on going to school at MIT or Harvard. It is simply too far, and unfortunately the crosstown buses are just not good enough. If you want to save some money, look at Allston and Somerville, or even Medford or Arlington (if you'll be at MIT/Harvard.) 
If you're going to be at Med School near Longwood, you can look at JP, though MGH, stick with my Harvard/MIT suggestions.)
I would generally suggest against university housing, especially for BU which has a well deserved reputation for ripping off its students. You should just look for a place in Allston/Brighton, or even in some of the cheaper parts of Brookline (move about a 1/2 mile from the T and you'll see the prices drop, not so far that you'll hate life, but just enough to save some $.) 

I want to be clear, my apartment is a freaking unicorn. Don't expect to find a studio anywhere outside of Allston or JP for under at least $1100 (which I would still consider a great deal.) I scoured the internet for months and pounced when I found it.
Finding much outside of Sept 1 will be hard. Consider coming to Boston, taking a sublet for a summer, and learning about the city. You'll be on site in the freak case where you find something as cheap as my place, but you'll also get a better idea of what you're able to find/afford. 
The realtor's fee is something that CAN be avoided, just do a search on craigslist that excludes realtors. It means your choices will shrink substantially, but they're horrible and nightmarish 20-somethings working solely on commission and they will make you hate life. I suggest not using them, not just to save money, but to save your sanity.
Don't live in JP if you're planning on going to school at MIT or Harvard. It is simply too far, and unfortunately the crosstown buses are just not good enough. If you want to save some money, look at Allston and Somerville, or even Medford or Arlington (if you'll be at MIT/Harvard.) 
If you're going to be at Med School near Longwood, you can look at JP, though MGH, stick with my Harvard/MIT suggestions.)
I would generally suggest against university housing, especially for BU which has a well deserved reputation for ripping off its students. You should just look for a place in Allston/Brighton, or even in some of the cheaper parts of Brookline (move about a 1/2 mile from the T and you'll see the prices drop, not so far that you'll hate life, but just enough to save some $.) 

I want to be clear, my apartment is a freaking unicorn. Don't expect to find a studio anywhere outside of Allston or JP for under at least $1100 (which I would still consider a great deal.) I scoured the internet for months and pounced when I found it.
Finding much outside of Sept 1 will be hard. Consider coming to Boston, taking a sublet for a summer, and learning about the city. You'll be on site in the freak case where you find something as cheap as my place, but you'll also get a better idea of what you're able to find/afford. 
The realtor's fee is something that CAN be avoided, just do a search on craigslist that excludes realtors. It means your choices will shrink substantially, but they're horrible and nightmarish 20-somethings working solely on commission and they will make you hate life. I suggest not using them, not just to save money, but to save your sanity.
Don't live in JP if you're planning on going to school at MIT or Harvard. It is simply too far, and unfortunately the crosstown buses are just not good enough. If you want to save some money, look at Allston and Somerville, or even Medford or Arlington (if you'll be at MIT/Harvard.) 
If you're going to be at Med School near Longwood, you can look at JP, though MGH, stick with my Harvard/MIT suggestions.)
I would generally suggest against university housing, especially for BU which has a well deserved reputation for ripping off its students. You should just look for a place in Allston/Brighton, or even in some of the cheaper parts of Brookline (move about a 1/2 mile from the T and you'll see the prices drop, not so far that you'll hate life, but just enough to save some $.) 

I currently live in Central Sq in Cambridge by myself and make about $2200 after taxes and other deductions. I pay about $900/mo for rent, which is unadvisable by financial standards but necessary if I want to be near my office and have my own space. The peace of mind is worth the extra % of my salary.
 
A note for finding cheap places: Have the money BEFORE you look at a place. If it is a deal, be prepared to put a payment down when you see the unit. I've had showings cancelled while en route to see a promising apartment, and had options disappear while I mull it over. The market here is cutthroat, especially when it comes to a cheaper-than-average listing. September 1 is city-wide moving day, and some places like to avoid the deluge, so you can find a steal in May. Your choices will be slim, but it can be a good time to negotiate a better rate. Same goes for the doldrums of winter. Locking in a place in January will likely mean cheaper rent or fewer fees, or a combo of the two.
 
As for transportation, you can get around the city on the university shuttles (especially Harvard and MIT shuttles) combined with a bicycle. The T only costs $70 a month for a pass, but if you're not using it frequently, you really can just do a pay as you go. I get free internet and laundry from my landlord, and I don't have cable. 
It's an expensive city, but it is also a city full of underpaid academics, so there are deals to be had everywhere. The cost of rent sucks, but then again, so does hauling yourself across Boston at 1am after a long day at school.