With all the open space in the lakes region you should be able to find someplace to let your dog run. Any school after hours, woods suitable for walking, etc. As long as you pick up after yourself (well your dog
) I really doubt you'll have any trouble with anyone. I hang out around Moultonborough when I'm up there and I have unlimited space and places to take my dog if I want too. Be creative you probably drive by many good doggie places and have never even considered them.