Unfirtunately, the wildlife do not coordinate their movements with the NH Tourism Bureau :-) You will spot them when you stop looking or least expect them. It also depends on what you hope to see. The quieter location, the quieter you are, the more likely they will come around. Fall is a good time for bird watching, especially as the hawks and water fowl start their migration. Mammals, small and large, are elusive but plentiful.
Check the NH Tourism website www.visitnh.gov for campgrounds. They will have good descriptions of location, setting, ammenities, etc.