Where to stay
Most major chains have hotels in Boston. If you stay in the Back Bay or downtown, you're only a short walk or subway ride away from major attractions (and most of the hotels are in these two areas). There are a number of hotels in Cambridge; they're also a short subway ride away. An alternative: B&Bs abound in the area.
In general, Boston is NOT a cheap place to stay. If you want to stay down, count on hefty charges (although there are a couple of relatively inexpensive places, such as the Milner and the Irish Embassy Hostel).
Also, in general, try to make your reservation as early as possible. There are certain times when rooms fill up particularly quickly: Patriots' Day (the Monday closest to April 19), which is when the Boston Marathon runs; the last two weeks in May (college graduations); July 4th (the Pops concert); mid-October (the Head of the Charles, which is to sculling what the Marathon is to running); and New Year's Eve.