Strongly suggest southern New Hampshire.
My grandparents are from Peekskill, I've lived most of my life in NYC, and spent the year before last in the Bay.
southern New Hampshire is close to very high end small towns like Exeter and Portsmouth. It's is somewhat reminiscent of the structure of the South Bay, but with a very New England feel. Peekskill is much more run down in comparison.
I can't speak to Bellingham, but in as much as you are interested in Peekskill or a non urban setting, southern New Hampshire is an extremely good choice.
Would be eager to help you gather more info about it.
Want to emphasize this point. Peekskill is in a partially recovered Rust Belt area, you will not find that many enjoyable activities, except after the ~2 hour train ride to NYC.
Portsmouth and a large number of towns in southern New Hampshire are extremely nice places by themselves, in addition to their proximity to Boston.