Having biked a ton in New England, I can say that Paul is right, the Cape has a great trail ( stay off of rt. 6).
My favourite runs are not on trails, but on lightly traveled roads. Rt.3 from the border south in N.H. is a neat ride, routes 10 & 12 along the Connecticut River are good too. My favourite in N.H. is the Kangamagus Highway. It is best to go west to east, and there are primitive campgrounds at Lincoln, at the base of the climb.It is the Rt. 112 between Lincoln and Conway, about 35 miles long.
In Vt. forget Routes 5,7 & 9. One nice ride is from Jeffersonville to Stowe along the 108, Smuggler's Notch, which also gives you access to the LT (Long Trail). There are campgrounds south of Stowe, a mile or so, Gold's Campground if I remember right. While south of Stowe, might as well get to Ben & Jerry's factory in Waterbury. St. Johnsbury to Littleton, N.H. across the Moore Dam is a nice scenic ride, large shoulders.
I do not use bike trails too often, but if you make it to Madawaska, Me. right across the river in Edmondston, N.B. is an 85 mile bike trail which ends up at the St. Lawrence River in Rivière-du-Loup. Have done the whole thing both ways.
Have biked in Ct.and R.I. but the traffic is pretty high and the bike trails rather short, however they may have improved them since my time down there (1997).
Feel free to PM me....be glad to help if I can.