Just gonna throw a bunch out there and let you check them out to your liking.

Rt 100 starts in southwest VT And runs south to north. Lots of great stops, little deli's and B&B's and cool towns to ride through. You can follow it through most of the state.
The App (Appalachian) gap is worth looking up. It's like a little tail of the dragon in New England. Except it's full of frost heaves.
Rt. 108 from Stowe headed north is very scenic. Also very busy/ touristy but very nice.
Rt. 105 running through Enosburg is a nice ride through farm country.It will take you around the back of Jay Peak and right up to a border crossing.
Rt. 14 running south through Craftsbury and Woodbury is a beautiful ride. This was our preferred way to head home from Stowe.
Just off Rt. 14 is a floating bridge. Really cool stop on the bike. I believe it's one of only a handful operation in the country.
St. Johnsbury is a cool town in VT to stop in.

In NH you have laconia, bike big place. Very crowded, lots of bikes, not my thing but lots of people like it.
Lake Winnepesauke has a ton of stuff to do around it.
The Kancamangus highway is "must do" ride through NH.