Many of the rivers and streams in New Hampshire that are north of Conway have very few aquatic insects and are for the most part quite sterile. That being said that is one of the reasons that most of those pretty mountain streams have so little wild trout and almost all the fish have to be planted.
I have fished the Swift River which flows West to East ending in Conway where it joins the Saco River. The Swift is a very pretty stream with lots of stocked rainbows. Another pretty little creek is the Ellis River which flows North to South. You can start at the Covered Bridge in Jackson and work your way downstream from there. There are lots of very pretty stocked brookies. Since the insect life is nominal the trout are very opportunistic and you can pretty much throw any attractor dry and expect to get a rise. Any nymph will work as will smaller streamers #8 - #10.
Another creek I used to fish when I was a kid is the Peabody River. This stream flows out of a ravine near Mt. Washington and flows north to Gorham where it joins the Androscoggin. The Andro is a fine river starting up in Errol and flowing south through NH and then heading East at Shelburne, NH and flowing into Maine.
The Andro is big water and has wild landlocked salmon up in Errol and good browns and rainbows down through the Thirteen Mile Woods, Milan, and again in Gorham.
There is a fly shop in NH that has a good forum. I think if you google Clearwater Fly Shop New Hampshire you should be able to get the site. If not PM me and I'll get it to you.
Ellis River
Pretty brookie