New to boston
Be aware that May-June is graduation season and hotel rooms are at a premium at this time. You might have better luck later in the month than earlier. Many hotels tend to hike their prices during this time since they know it's the height of the season. I would check with one of the online reservation services (Expedia, Travelocity) to get rates. Good luck.
re: Eric Eto
I agree that June is a tough time to find a deal in Boston. Most of the Boston/Cambridge hotels will be asking upwards of $200 a night during this time. If you have a car, you can save some money by staying outside the city (Hampton Inns, Courtyard etc.).
As a general rule, Cambridge hotels are a bit less than most Boston properties if you need to be "in the city". I suggest you call Citywide Reservations at 617-267-7424. They can advise you on all area hotels and book a room for you too.
This is what I send to people visiting our lab, all on the cheaper side (such as it is in Boston).
The place I most often have people stay at is the Buckminster Hotel in Kenmore Square (645 Beacon Street, 617-236-7050). Their rates are seasonal and depend if there are functions going on in town.
This hotel is the most convenient to public transportation. If you're taking public transportation from the airport, you would take the blue line first then change at Government Center where you'd get the green line, either the B, C or D line to Kenmore Square and it's about a two minute walk.
The place closest to Dana-Farber is the Best Western at Children's. Their number is 617-731-4700 and the price is usually about $209. There's another place we've used, the Beacon Inn (1087 Beacon Street, 617-566-0088, 888-575-0088). They have rooms with private and shared bathrooms.
Some other places include the Beech Tree Inn (617-277-1620) (fairly close walk to DFCI but not quite as convenient to public transportation), Coolidge Corner Guest House (617-734-4041), Brokline Manor Guest House (617-232-0003, 800-535-53235)(further away and maybe kind of funky) and the Howard Johnson in Kenmore Square (617-267-3100) and one by Fenway Park (617-267-8300, HJ toll free 800-446-4656).