In NH you can see a Naturopath as your primary care doctor. Unfortunately, the conscientious belief bill has been voted inexpedient, so it may not make it. http://www.vacchoicenh.org/
has all the information on this bill.
For health food stores, the middle of the state is fantastic. The Co-op in Concord has wellness classes, Granite State Natural Foods has a good selection of herbs, A Market in Manchester has some good variety, and the Natural Choice Market in Hooksett is great.
The Concord area is actually getting really progressive. We've got a couple of great natural products stores (Real Green Goods & Your Home Your World), an independent theater, bus service (though limited), phenomenal farmer's and art markets during the summer, etc. Not sure about the homeschooling community here (I'm still expecting), but there are a bunch of homeschoolers out in the Weare/Goffstown area, not too far.