FWIW, MA is a bit different in that if a restaurant has a liquor license, BYOB is illegal. (If they don’t have a liquor license, the legality of BYOB depends on the city/town they reside in.)
You’re going to want to go out to the store in Waltham - they have fantastic tastings. Their grand tasting in October is always a blast, and, though I haven’t lived in Boston for a few years, they had a great series of Saturday tastings in the fall with typically 6-15 wines and the quality was always high.
I’ll add to the recommendations of Marty’s and Federal Wine & Spirits (don’t be put off when you walk in - the fun stuff is mostly downstairs).
Another place that’s well worth checking out is Ball Square Fine Wine in Somerville. They are smallish but have a very well curated selection, including a nice range of Greek wines (the owner is Greek). They also have a good annual tasting, though it gets crowded.
Brookline Liquor Mart, The Wine Emporium, and Blanchards are all worth checking out at least once - I’ve had some good finds at all of them.
Avoid Central Bottle in Cambridge. Their wines are good (if narrow) but the prices are tear-inducing.
Definitely check out Ansonia in Newton. Father/son importers of mostly French and Italian wines. I don’t live in Boston but we were there this past April and spent a good hour there on Saturday afternoon.
As much as I liked Central Bottle and Liz (the owner) was great, Social Wines does a much better job at bringing in some of the more highly-allocated natural wines, while also being able to cater to a more mainstream buyer. Definitely worth popping in the new Cambridge shop if that’s more accessible than the original in Southie.
Marty’s and Gordon’s and all above mentioned. However, the gem of a store I have found is all of the way out in Lenox (far west of the State). Owned by Jim NeJaime (not to be confused with NeJaimes in Stockbridge or Downton Lenox) is Spirited of Lenox. Jim is a tremendous wine guy! He is knowledgable and extremely helpful. He also retains the buying power of a business that goes back to Norman Rockwell paintings of downtown Stockbridge. If you are ever there (sorry Jay I had no idea you were going) make sure to meet him. Otherwise, call and introduce yourself, and get onto his personal email list. Literally, if there are some really special wines you want to get now, or as they are released to stores in MA, he can go ahead and snag them at very competitive pricing (will always match or beat pricing). He has tremendous access, and will do special ordering for customers, and although he has a very nice shop on I believe Route 7 in Lenox… the best wines are often sold to customers on his lists and may not hit the shelves. And, he does some direct importing, lots of great tastings in store and restaurants, and does ship!
Flew some burgs from CA to Boston then found out no BYOB. We had a pre-dinner hotel tasting in paper cups having used a horrible corkscrew to begin with.