Go to Boston if you're in Southern NH.
Kancamagus Highway area is beautiful for sightseeing, hiking, etc.
Lake Winnepesaukee/Weirs Beach area in the lakes region.
The foliage should be nearing peak in Northern NH by the end of September.
Do you have children? Santa's Village is so fun.
Lots of opportunities for shopping in southern NH (Rockingham Mall (Salem), Pheasant Lane mall (Nashua)) and outlet shopping (Laconia). NH is tax-free, so buy some clothes.
I live 10 minutes from the southern NH border. Have fun!