There is no organized way of even helping a new predoc to find a place to live. For example you cannot get into Harvard dormitories. In many cases predocs have had a friend, or a friend's friend, to stay with or get some other temporary place for the first days to be able to start looking for an apartment. If you are coming and don't have anything organized and don't know anybody, try contacting the secretary of the division you are going to be with. You will need a letter from your division secretary stating your affiliation with Harvard to be able to get in.
Prices are higher in Cambridge and certain parts of Boston than in eg.
The same problem might come up also when renting from individual land-lords. As a consequence, you need additional patience and time when looking for housing for a whole family.