May be a ride for you, but we enjoy visiting the base of the Cog Railway station. We do not go on the trip, due to the fact we have three young kids and it is quite pricey. However, we enjoy going to let the kids see the train and watch it leave. There is a nice shop and snack cafe there as well. Also, the ride there offers some cool views and waterfalls to check out.
We always make a day stop in downtown North Conway and enjoy visiting the shops and seeing the train there as well (not too pricey for the shorter ride...).
Even though not free, I am sure you are aware of Clarks Trading Post...We make a point to get that attraction in each time we go to NH. One last thing...Not sure of your direction of travel, but we found a great diner in Tilton, NH just off 93 called the Tilton Diner. Kinds of 50's decor and good homemade food...Maybe give it a try? Have a great visit! Nice to hear other DISers enjoy visiting some of the same "other than WDW" vacation spots that we do!