As someone who grew up in the Granite State (or the Shire, as many of us fondly call it, that should tell you something) I can confidently say it may be what you are looking for. The economy is still decent (lots of small business, too). The crime is very low (some issues around Manchester, or Manchvegas as we call it, but nothing compared to say... Baltimore), the only man-made disaster you might have to worry about is the nuclear power plant in Seabrook, but nuclear power is very safe nowadays. Then there are the natural disasters, I have one question for you regarding that: do you like snow and if so how much? Because we can get a lot of it.
If you live in the southern area of the state you'll be a comfortable distance from Boston, far enough to not feel it's negative effects, close enough to travel to and enjoy (a really nice city, BTW). You will be surrounded by awesome get-a-ways spots in Vermont and Maine, too! Not mention both of those states aren't too bad to live in... I miss home!
New Hampshire does have a hefty property tax, but every other tax is pretty low or non-existent.
Wow, I could write a lot about this. I'll stop here and leave you with this: definitely check the area out.