Central VT is GORGEOUS. Personally, I like the areas just south of Waterbury and Stowe -> Waitsfield, Warren, Moretown, Duxbury area. Those areas are close enough to Burlington (bout 45 min - hour)and the interstate but far enough away where you get some solitude. I plan on moving there myself but I am actually making a move to NH I think, for a few years.
In NH, I would say the White Mountains. Absolutely beautiful area. Avoid Conway and anything in the immediate proximity as it is a HUGE tourist area. My family had a house in Bethlehem NH for many years and that's a great area. Nice scenery up there. Cold winters though. Anything in Franconia Notch is nice but some areas a touristy. Places like Sugar Hill aren't bad, Bethlehem, whitefield. Close enough to Littleton (shopping, Wal-Mart and Corey's gun shop
) but out enough where it's quiet and fairly cheap. Can't beat the views from those areas.
In both states, pay attention to where the ski areas are - that's where you are gonna get real touristy. Stowe in VT - near the village can get busy but the outskirts are nice. In VT, you rally only have to worry about the immediate area of the tourist attraction where NH you have to pay attention to the surrounding areas too. I am speaking for Central/Northern VT. I wouldn't be caught dead living anywhere near Killington or Okemo.
As far as being pretty close to NYS border - check out Bristol, Vergennes, Ferrisburg, southern Hinesburg, Charlotte or any of the Islands.
What kind of living you looking for? North Western VT/Islands is flat, central is pretty "bumpy"....