Housing in Cambridge and Boston is quite expensive, and the market is very active. Most rentals are yearly, and start on September 1st, but there are many sublets, so it is possible to find a place after arriving in Cambridge- and stay in an Airbnb while you search for it—but it is better to look for it in advance.
Rents range from $ 500-1000 for a room in a shared apartment. Somerville, Watertown, Allston and Brookline and other locations along the subway line (known as the “T”) are relatively cheaper alternatives (see maps). Biking is quite common—but the winter is VERY cold.
As a visiting student, you can access on MIT on campus housing just in case of vacancy after regular students have been accommodated. Several Rocca fellows have succeeded in staying at graduate dorms and have liked it. If interested, contact the MIT housing office, regarding both their on campus graduate options and their off campus listing. You will need your MIT student ID for searching the listings and for on campus confirmation, but you should contact them in advance.
As with other matters related to coming and staying at MIT, current or former Rocca Fellows can be your best resource. Once awarded a fellowship, reach out to other Rocca Fellows who are currently at MIT or recently left it for housing tips.
The Association of Italian students at MIT (mostly PhD.s and Post-Doc students) also offers a very helpful set of information about settling at MIT. You can reach out to them: you will probably want to join them after arriving.