There's good news and bad news: I came across the website Pedaling.com, which has lots of cool features. You can search for rides by state, region, trip length, terrain and more. You can even set up a trip planner to take with you. I like all that!
The bad news is there aren't many rail trail options listed for New Hampshire. But you just may find something to your liking here. I'm trying to get up the courage to take an on-road trip, somewhere with light traffic. This site lists some good possibilities and may just be the push I need.
While we're on the topic of biking...I have a really ambitious trail I'm adding to my wish list. The province of Quebec has a 2,700 mile network of bike trails! The Route Verte, unveiled in 2007, stretches from one end of Quebec to the other, passing through 320 towns--obviously, I'm talking about biking just one tiny portion of it. I first read about this amazing network in the Boston Globe. I think it's fair to say you can see a little of everything along the Route Verte: lakes, canals, farmland, forests, historic forts, churches, and more.
There's even one 30-mile loop that's "sprinkled with works of outdoor art." There's a website devoted to the Route Verte if you'd like to read more. Personally, I find that site a little overwhelming since I don't know the area. I prefer reading descriptive narratives like the one I read in the Globe. See you on the trail!