The city has enough Irish heritage that you really can't go wrong no matter what you do. There's a pub every few blocks, so I'd recommend finding a neighborhood you like and bar hopping. It's more enjoyed with spontaneity in my experience, and you'll make plenty of friends along the way.

Just be aware, that many pubs will have a cover charge in the touristy spots like Southie and around Faneuil Hall. Follow the music and have fun!