I was curious to know what is currently the best source (or the best sources) for information about people indigenous to the Americas prior to European contact. I am especially interested in the area around where the Massachusetts Bay Colony would be formed.
Can't help much with the Massachusetts area, but if you're interested in pre-European America in general, I definitely recommend the book 1491 by Charles Mann.
As Michael points out, a lot of what we know is based on European accounts. And those authors had their own axes to grind, consciously or not - a man trying to turn the local hunting ground into a farm is going to see (and say) different things about the locals than a priest who hopes to convert them.
Even today, with less material interest in the issue, people often tend to either demonize or romanticize foreign cultures. 1491 tries to avoid this bias by using archaeology and related disciplines to study precontact American culture on its own merits.
I wouldn't say Mann has no bias - he's out to show that there was a higher level of civilization than people generally assume, in both North and South America. But he is pretty good about separating evidence from speculation, and he brings together a lot of very interesting research that I hadn't really seen anywhere else.
You could look at the diaries of the colonists of the time, such as Anne Hutchinson who was captured by Native Americans, or John Winthrop and see what they note about the natives at the time. The problem with many of the tribes in the Massachusetts Bay area is that many were displaced by the Bay Colony and from diseases that were rampant up and down the New England coast. Many tribes did not leave much in the area, and other than Connecticut and Maine you won't find any major areas held by Native American Tribes. There are small tribe holdings in the other New England states but not very significant and not much in the way of museums, but you can check locally or go to the tribes and try to talk to leaders. You can check diaries of the Plimouth Plantation founders and anyone who fought in King Philip's War, as well as the local villages as noted previously to find out more.
While most of this is after contact, the written word from the tribes is lacking from the time, since most had oral histories. So anything that might be put down would be from the Europeans.
I would start with local historical societies. Usually towns, counties or library districts have these. You'll likely find specific information that will be of interest, but more importantly, references to primary sources.
For a lower-labor approach, look for college classes on local history and call up the professors.