Brookline is a fascinating town to live in. It is one of the safest places in Boston area, very quiet, peaceful and residential. But do not be fooled by its seeming serenity. Just take a trip to the Coolidge Corner and you will most surely enjoy local indie movie theater, company of joyful students, various restaurants and summer concerts.
In terms of places to live, you have a wide variety of options from luxurious Longwood Towers to a room in an old historic house filled with student renters. Brigham and Women's Hospital is nearby - easy 10 minute walk or just few minutes on a bike. Trip to MGH is easy too - any green line subway will get you to the Government Station from where MGH is only a short walk away (or you can switch to the red line and enjoy the T for one more stop). Once again, if you choose to bike, a wonderfully scenic 27-30 minutes ride by the Charles River awaits you.
In terms of finding the right place, local listings and Craigslist are your best friends. Keep in mind that getting around in winter time may become a bit more challenging in the snow. But no worries, Brookline city authorities are excellent with cleaning the streets so their beloved citizens travel safely. T-stations are abundant and there is always at least one within 10 minute walk. If you have a car and still planning to keep it after moving to Brookline, ask about availability of parking spots well in advance, since not all places can provide it. Hope you will consider Brookline as your favorite hibernating place while in residency!