Toward the end of our 2 week New England trip in September my husband and I will travel from the White Mountain area (Lincoln) to Providence. Any interesting stops along the way for the day of driving? Or even an overnight stay? Current plan is to spend 2 nights in Providence before flight home.

Just south of Lincoln is an easy hike with beautiful views:
Hike New England - West Rattlesnake Mountain

Lunch at Pickity Place in Mason...reservations needed
https://www.pickityplace.com/

Art museum in Manchester...you can also visit a Frank Lloyd Wright house
Currier Museum of Art | Focused on Art, Centered in Community, Committed to Inspire

Lowell NHP
https://www.nps.gov/lowe/index.htm

We did the Providence food tour last September and it was a lot of fun even in the rain.

I assume that with so much time spent in the White Mountains that you will have done a loon tour on Squam Lake and visited the distillery in Tamworth.

You didn't mention your interests. If you didn't do a boat tour you could head to the coast for an inland rivers boat trip out of Portsmouth (or the harbor cruise) then continue south on I95. Side trip to Salem MA and the Peabody Essex Museum.

Lowell NHP is great. Lunch at Picket Place is very popular - check out their menu which changes monthly. There are three seatings.

Canterbury NH Shaker Village tour.

Concord MA and Fruitlands

Last year on our quick trip through NE, we spent a night near New London CT. The next day we spent several hours at the US Submarine Museum. I took a self guided tour through the Nautilus (the first nuclear submarine). You can make a donation on the way out but otherwise all free.

Thank you for these great ideas! This will be our first time in NH and glad to have so many options.