I'd suggest the Porter Square/Davis Square area in Cambridge/Somerville. On the Red Line (about 20-25 mins to Back Bay sta, which includes one train change), in a lively-but-not-rowdy, ethnically-diverse neighborhood filled with shops, restaurants, food outlets, young professionals, students, and just about anyone else you can imagine. (Except Republicans, maybe.)

Also an especially bike-friendly part of town, both on the streets and with access to the Minuteman Bikeway.