If you got on the Turnpike westbound at Brighton, you were right at Beacon Park. The main line of the B&A ran roughly parallel to the NYNH&H for a short distance out of South Station where it broke off to go through the B&A side of Back Bay Station. The New Haven called their side Back Bay, the B&A called their side Trinity Place; the B&A always did things a bit differently.
Trackage arrangement today is somewhat similar as the Framingham / Worcester commuter trains use the B&A as does Amtrak 448/449. It was a straight shot from the B&A coach yard (which is roughly where the Prudential Center is today) to South Station.
Memories of Beacon Park for me include multiple sets of NYC E units for passenger trains, FAs for freights, Alco RS units, etc. etc.
The B&A in Boston also at one time passed behind two major league ballparks; Braves Field (IIRC, it's now Nickerson Field and belongs to Boston University), and behind Fenway Park.
Things were, of course a lot different before they ripped up everything for the Turnpike.
I was still living in Boston in the PC era; Beacon Park was a place to find 6-axle Alco beasties (ex PRR) and lots of other stuff from what were once "foreign" roads. This trend continued into Conrail with RDG and EL power being fairly common. It was a hard place to get into to take pictures, even "back in the day," but I managed to get more than a few, due in large part to a friend who worked there.
You'll want to check out Robert Jones's 2 vol. set on the B&A; pricy, but well worth it.
Hope this helps