Having lived in NYC and also visited BOS, flown to both cities on BA in F I would suggest the following:

Open-jaw (as suggested by others LHR-BOS/JFK-LHR).

F to BOS with CCR access at LHR, spend 3-4 days in Boston.
Boston is a really nice city with lots of heritage, history and culture. You could do a week there the first time. So much to explore and see in the region.

Take the train, a plane or a hire a car that you drop in NYC. The drive down from Bos to NYC via Providence and the coast is nice.
NYC can be done in 4 days but for first timers a week is good. There is so much to see, do, experience and eat! My advice for NYC is don't stress. Part of the experience is just being there, feeling the ambiance, gazing at the buildings.

JFK CCR is actually really nice and I prefer it over LHR. While a rather short flight, if using Avios it is still decent value. And arriving at LHR you can unwind in the Arrivals Lounge which has a dedicated CCR dining area.

Make it two weeks if you can.