Boston is a wonderful city - definitely worth a visit. Not far to Salem (also worth a visit in the summer, but not much going on in winter for anyone else reading) and just over half an hour on the train to Providence.
I found Boston's transport system very straightforward & reliable
I'll second all those points.
As well as the scenic coastal suggestions mentioned up thread, that part of New England also has some historical interest focused around the American Revolution.
I lived in the Boston area for a time and spent some of my weekends pottering around nearby towns in Massachusetts such as Concord and Lexington.
Admittedly, I did this by car, but you can get to both places from Boston by public transport (Concord by the hourly Fitchburg
* commuter rail line from North Station. Lexington by the Red Line Subway to Alewife then a ~20min bus connection).
When I visited, it was interesting to experience the differences in history as taught in American versus British schools. No great surprise, when you think about it; Britain lost out, so best to keep a bit quiet about it. Visiting a couple of sites and a museum (in Concord I think) I realised I knew very little about some significant events which would be second nature to most native-educated Americans.
For example, in one place there was a detailed account of
Paul Revere's Ride - a topic I was completely ignorant about, but which was so mainstream in the US it didn't warrant any explanation of the basic background at the museum.
Maybe it's like an American doing a self-guided tour of Kent and thinking "I've heard about Hastings sometime, but can't remember why. But who's this William the Conqueror guy? And why do they keep banging on about 1066?"
* Just noticed that off-peak stops at Concord station are noted as 'flag stops'. So, inform the conductor or flag down the engineer - the
f indication in timetables being equivalent to 'x' in Britain.