If you come to Dedham, there's the Dedham Historical society in Dedham Square which has a large collection of Dedham Pottery on display and artifacts from colonial days. The Fairbanks House in Dedham will be open soon. It is the oldest wooden structure in North America and is not far from the square. Tours are every hour. You can find both on the Web if you do a search.
Every town has a cemetery, usually located near the square.
Tombstones go back to colonial times an interestingly enough, some are in better condition than similar ones in downtown Boston since they have been respectfully ignored in the suburbs. Most of the churches date back about 100-150 years. There must have been a building craze back because I don't know of any churches older than that. Probably the Puritan fore-fathers forbade any kind of fancy places of worship. It's easy to get to Boston via the commuter rail from Dedham.