Well, I'm one of those New England folks. There are lots of possibilities. There are good parts of both New Hampshire and Vermont (as well as Mass and Maine), so I wouldn't rule anything out except probably the more urban areas. Vermont is picture-postcard-like if that's what you want (it's my preference), but NH also has the White Mountains area which is nice (take a look at Jackson, NH).
A couple years ago when my wife and I first got into biking, we hooked up with
these folks and did a 3-4 day tour in Vermont. They provided the maps, routes, etc. and shuttled luggage between the inns. It's typically more than 10 miles, but they can probably accomodate anything. Around Lake Champlain was nice (and not too hilly)
Another idea is just go hang out in one place and pedal around town. We did this one foliage season and it was really nice. We were at an inn in the "Northeast kingdom" area of Vermont. Spectacular foliage although I'm glad I had low gears on the bike! This sounds like it might be the ticket for you.
One thing to bear in mind is that "foliage season" progresses from north to south. It can be 2-3 weeks or more for the "peak" to progress from Canadian border to Boston area, so try and time it accordingly. Weather can be, unfortunately, hit or miss -- we've had foliage seasons that are more spectacular than you can imagine, and others that are cold and rainy.
Feel free to ask questions or PM me if you have questions.