How about the Franklin Pierce Homestead in Hillsborough, NH (childhood home of our 14th president).
http://www.nhstateparks.org/state-parks/alphabetical-order/franklin-pierce-homestead/

Strawberry Bank Museum in Portsmouth, NH
http://www.strawberybanke.org/

I am sure there are many other more good suggestions, and I hope others will chime in.
I have never been to the Franklin Pierce homestead myself, and but it is now on our to-do list

So is Canterbury Shaker Village
http://www.shakers.org/

I would consider that that site, Strawberry Banke in Portsmouth and Shelburne Museum in Vt require fairly big time commitments
Shelburne Museum has a huge collection and it really takes at least a day to see even the highlights
http://www.shelburnemuseum.org/

Another interesting place to do visit next Saturday (Oct 3) is Castleton, west of Rutland. They are offering tours of many buildings for Castleton Colonial Day
http://www.rutlandherald.com/article/20090925/SPORTS/909250313/1007/SPORTS

What was the Franklin Pierce homestead we saw in Concord, NH, if his childhood home was in Hillsborough, NH?

And just want to agree about the Coolidge farm -- it's a gorgeous setting.

The Franklin Pierce place in Hillsborough is his birthplace and childhood home. The Concord house is the one he owned and lived in as an adult.

Appropriate topic Vttraveler for this time of year. I wonder when leaf peepers get tired of just driving around looking at leaves and would like something else to do. We keep meaning to visit the NH History Museum in downtown Concord while the kitchen exhibit is still on display. I haven't been to the museum in quite some time but still remember a fascinating exhibit on making socks with a 'new' knitting machine. Women could work at home and children were expected to help but the heels still required some handknitting skill.

Hippo Press is a free weekly newspaper that is pretty good at advertising events and things to do in the Nashua, Manchester and Concord. When we travel we always pick up local papers to find things to do. We have never been to the Raptor Migration Observatory at Miller State Park on Pack Monadnock in Peterborough NH. Recently the public was invited to witness the release of two rehabilitated hawks, one at Pack Monadnock, the other at Carter Hill Orchard in Concord NH. I was amazed at the number of hawks that are counted in a single day. We like to watch our local birds but apparently there are some places that are like interstate highways for birds.

Oct 4 is Harvest Day at Musterfield Farm in N Sutton NH. http://www.musterfieldfarm.com/ This is a small farm museum that I think is best enjoyed during a special event. And, it's not that far off Rt 89.

Also convenient to Rt 89, Mt Kearage Indian Museum in Warner NH. http://www.indianmuseum.org/

The Indian Museum has been on our "to do" list for quite a while but we never manage to build in enough time when we are driving that way.

When I was putting in the link to Shelburne Museum yesterday I realized that there are a number of good temporary exhibits there now including one on Tiffany.

I realize I should also have listed Shelburne Farms
http://www.shelburnefarms.org/comevisitus/index.shtm
It and the Billings Farm museum are especially good for kids who would enjoy the farm animals.

More - not well known places:
Hemmings Motors News, store and classic car display, Bennington VT
King Arthur Flour store, Norwich VT
Burdick Chocolate, Walpole NH

Last night I saw a short segment on the Justin Smith Morrill homestead on Vt public television. I told my husband it looked interesting and we should go there sometime and he informed me he had been there with one of our friends a few years ago when they took a day off to go leaf peeping. He recommends it. It is open through Columbus Day weekend.
http://www.morrillhomestead.org/

All these suggestions are great. My printer has been active and I will file them in my to do list.

A great place to go in the NEK Northeast Kingdom of Vermont is the old stone house in Brownington, Vermont. They ofter have events and consists of several buildings. Our guests went there yesterday for an apple and cheese festival and loved it.www.oldstonehousemuseum.org

Listening to the Loons on Seymour lake , Morgan, Vt as I type this. The color here is fabulous.

Sorry the link is www.oldstonehouemuseum.org

oopsie - try this
http://www.oldstonehousemuseum.org

This coming weekend is Octoberfest at the Harpoon brewery in Windsor, Vt.
harpoon brewery oktoberfest
We plan to go down to sample some beer and tour the brewery, and also hope to visit the Consitution House and/or the American Precision Museum in Windsor
http://www.historicvermont.org/constitution/
http://www.americanprecision.org/

There is also a Simon Pearce glass factory in Windsor
http://www.simonpearce.com/CSTM_WindsorWorkshop.aspx

I forgot to mention that I think the old Stone House Museum was where we visited a few years ago to see an antique engine show. DH likes to attend antique tractor shows, some are called steam ups. Some shows are mostly tractors, others are mostly steam operated engines. Sometimes they include plowing, a parade etc. The year DH took his dad on a weekend trip to the Eric Sloane Museum in Kent CT they happened to choose the same weekend as an antique engine day. They were thrilled. A lot of these events aren't well known and are poorly publicized but can be found by doing some googling. We haven't visited any of the logging museums in NH but the Leonards Mills Logging Museum near Bangor ME is very interesting during an event day esp when the guys who restored the saw mill are present and the college teams are having wood cutting competitions.
Sorry, this isn't about NH and VT but I want to encourage people to search out those great but not well known events. A sheep to shawl competition is very interesting and it's literally what it says. The wool is sheared off the sheep, spun and knitted into a shawl during the day. Sometimes the knitting is a group effort. And I love border collie sheep herding demonstrations. What great dogs!