We stayed in a really nice KOA near Quechee VT. last summer, people were very nice and the sites were roomy, we stayed down in the lower part. Quechee is near Woodstock. The Simon Pearce store in Quechee is a great place to watch glass blowers and they have many beautiful hand made things for sale, also a great restaurant. Woodstock is also delightful with lots of quaint shops. Sugarbush Farms is a great place to buy cheese and maple syrup.
Any specific part? I stay mostly at VT State Parks (no hookups) and they each have a different personality. They have a 14 day maximum at any one park. You can see all 52 of them at vtstateparks.com
For hookups, North Beach in Burlington VT. Very popular, may be tough to get a reservation for a month. Shelburne Camping Area is terrible unless you don't plan on being there at all. Moose River in St Johnsbury VT is awesome-great folks, super well kept up and free homemade donuts and coffee every morning. If you have an idea of which part, I could probably help you out more.
Haven't stayed in NH. Still exploring my home state of VT. Enjoy!