This obviously depends on your personal preferences. If you're a young professional, College Hill or downtown proper would suit your needs just fine. Downtown is small, and not a ton of bars and restaurants (compared to bigger cities such as Boston or New York), but you can probably find cheap housing there (many apartment complexes were built and left empty during the housing boom of the mid-2000s).

College Hill, obviously, is a slightly younger demographic, as the name suggests.

If you're looking for more of a suburban environment, any of the towns to the north and east would probably suit your needs. Mansfield and Foxboro, MA are big commuter towns due to their location on I-95, each with many suitable apartment complexes.

Me personally? I'd live in Boston and commute. But I can understand why that would not be ideal. It's hard to say without knowing more about you.