You'll be pressed to find a new-ish single-family in Salem for $600k, unfortunately.

Haverhill sounds like it would meet a lot of your specifications. It does not give the same quaint vibes as coastal Maine/NH though, be forewarned.

If you can push your budget closer to $700k you might open up some options closer to Boston like Norwood, Beverly, or Hudson which would have better transit than Maine/NH, too.