I can recommend tons of places, and I'm sure others can as well. Where exactly in Boston are you going, Boston proper? I actually haven't been out much in Boston itself, and I'm not familiar with any BYOB places. But here are some of my recommendations for some places surrounding Boston:
Allston/Brighton:
Sunset is a big bar with a zillion taps and decent food. The draft selection isn't very inspired or organized however, and they'll be out of a good bit of it. But they do have a lot.
Deep Ellum is one of my favorite bars, ever, it's a true gastropub. Much smaller beer list but very very well picked, and the food is beyond incredible. The service is great (they know their beer) and they have a really good whiskey/cocktail list as well.
Cambridge:
Cambridge Brewing Company (aka CBC) has been voted the best brewpub in the country before. They have amazing homemade beer and decent food (solid burgers). They just started bottling in the last year I think, but there used to be only a few places in town where you could get their beer. So if you want something that you can't get back home, you might want to head here. A lot of their stuff is seasonal, and most of it doesn't get bottled. Plus I'm not sure how far their distribution goes.
Lord Hobo: Nice gastropub, same type of place as Deep Ellum. Good food, great beer list and awesome cocktails as well.
Meadhall: this place has a ton of taps and overpriced food. Like Sunset, they boast a lot of taps but it's not the most inspired selection and they're always out of things.
Somerville:
Redbones BBQ has a really fun bar area (complete with a "wheel of fortune" style device, but to help you choose your beer!) with some great beer. The food isn't mind blowing but it's not bad.
I used to live in Somerville so there are a lot of other places that I like, but most of them are more neighborhood type places.
I'd recommend Deep Ellum, CBC or Lord Hobo if you're picking one place.