Boston is one of my favourite cities, and has tons to do. Very different to NYC, and much smaller too. It isn't known as the walking city for nothing. PM me if you'd like more details, I'm also GLA based : ). Salem and Harvard are short trips from there too.
Hotels can be expensive, i've stayed at the Revere (Decent), Indigo (basic but OK) and further out the Holiday Inn Bunker Hill area. It was OK, but far cheaper than in the city, even when factoring in an Uber there and back. Or the orange T Line is a five min walk, and you'll want/need to use the subway at some point in any case.
Back on the BA subject, the lounge in BOS is excellent. I've used the F Dining a few times too, and also connected from/to GLA. All on Avios, a great redemption IMHO.
I'd stick with your original plan.