The best places to see in New Hampshire, in my opinion, are Franconia Notch (the middle of the state), the Connecticut Lakes, which are along the NH-Canada border, Kancamagus Higway, which runs from Lincoln NH to North Conway NH, and the Monadnock region in southern NH (not too far from Manchester).
As for B&B's, I haven't stayed in the Machester area, but I have stayed in North Conway several times. I'd recommend the Eastman Inn. I stayed there and really enjoyed my stay last year. The place was clean, they had great food, and it was centrally located for the Mount Washington/North Conway area.
Hope this helps!