Doesn't leave many options. In areas where the chains have moved in, the old little independent motels tend to be outdated and lacking in some basic comfort amenities we expect from lodging these days. They can't keep up. As for B&Bs, in rural New England this is part of the stock and trade of tourism. There are some larger inns that are old and well kept, if that would afford your husband a bit more anonymity. But really, part of what Inns and B&Bs are selling is the personal touch, connection, hominess.
So... There is the Valley Green Motel and The Coach House Motel and Cottages, both in Keene. I stayed at The Coach House close to 30 years ago, when there were no chain hotels in Keene. Don't know what it is like now, or how it would compare to the chains.
Inns are larger than B&Bs. There is the Chesterfield Inn, on Rte 9 a couple miles east of the bridge from Vt to NH. The Hancock Inn, in Hancock NH, claims to be the oldest continuously operating inn in the country, or something like that. Very nice place. The Jack Daniels Inn in Peterborough is a nice place. Not really an "Inn" like the above two. Used to be called a Motor Lodge back in the day, but they have definitely modernized along with their name upgrade. The East Hill Farm in Troy is a wonderful family oriented resort with a modern rustic feel on a working farm. Your 2 1/2 year old will love meeting and feeding animals and lots of other activities they have for families.
I am sure that I am missing others. You can Google <Monadnock Region Inns> or check the NH Tourism site www.visitnh.gov and look at their lodging link for the Monadnock Region.
Keep in mind that the Pumpkin Festival is a big event around here and lodging fills up quickly. You may find that a lot of lodging is already fully booked. Good luck.