Tons of good spots that might be off the mark a little.
- Parish is a late breakfast/lunch spot at the end of Boylston St next to the Public Gardens, great selection of beers and one of the best sandwich menus around
- Bukowski's is at the other end of Boylston St near Mass Ave, unbelievable selection of beers, and right next to a great bowling alley/pool hall
- Lord Hobo across the Charles river in Cambridge is probably the most famous beer bar in Boston, and it IS fantastic but usually packed and WAY over-priced, go if you're in the area, but not a necessity
- Allston, "west Boston" area is easy to get to, and has two relatively low key beer bars that are outstanding; Sunset Bar and Grill, something like 96 taps and a great Mexican food spot, and Deep Ellum, a little bit of a hipster crowd and right next to a metal venue, so be careful of event nights, could be a rough crowd.
Out that way is the Publick House in Brookline, on a street with loads of fantastic restaurants, good spot for pre or post dinner beers, but depending on where you're staying, it could be a hike
Steer clear of the tourist traps like Fenway where the Boston Beer Works is, mediocre beers charged at exorbitant prices, but go on game day if the Sox are in town, unbelievable atmosphere
Not beer bars, but a few good spots are The Littlest Bar, Green Dragon, and Roisin Dubh in Fanueil are all fun at night. The Crossroads pub at Mass Ave and Beacon is an actual "Cheers" bar, not like the tourist trap one, great craic.
Out in Brighton, on Washington St, there are three pubs all together that are loads of fun on a Friday or Saturday night; The Green Briar, Devlins, and Porter Belly's. The Briar is typical Irish pub, but great craic after 10-ish. Devlins is a great spot for dinner, and a solid above average beer menu. Porter Belly's is post midnight drinking at it's finest.
Harpoon and Sam Adams have tours available in the city but if you've ever been to the Guinness Storehouse, they're similar, not exactly authentic, charge way too much, but it's fun.
North Boston is a wasteland for beer, unbelievable Italian food and wine, but nothing for beer. Southie is good craic and as close to drinking in Ireland as you're going to get abroad, but not too much in the way of good beer bars. You're best bet for a random spot that has a good beer menu is Cambridge, Allston, Brighton, Brookline, and some spots in the City Centre. Definitely check out Ratebeer for places locally where you're staying.