The Scottish Rite Masonic Museum & Library is an underrated museum at the southern end of Lexington, covering American history from the colonial period onwards with a particular focus on the Masonic connections of the Founding Fathers. The permanent collection includes prints, paintings, decorative arts, and artefacts relating to American history and culture, and the temporary exhibition programme is genuinely interesting.
The museum is larger and more professionally run than you might expect from its niche remit. If you have already done the Revolutionary War sites and want something different, this is a good option. Free admission. Located about a mile south of the Battle Green on Massachusetts Avenue.