Keep in mind peak foliage time is first thru mid of Oct in NH and Maine. You might be able to rent a cottage/cabin for a week in NH's Lakes region but keep in mind many are uninsulated and Columbus Day weekend is a traditional time to close up for the season, drain pipes, etc. However, there are also probably a lot of vacation homes there are year round. We have gone thru a rental agency that services Lake Winnipesaukee/Lake Winnisquam area. We like a rustic cottage with a fireplace. If you rent on the north side of Winnipesaukee it is less congested plus you are closer to the mountains. Center Sandwich is a beautiful area/also Squam Lakes area. Haven't been to Remick Museum in Tamworth but see weekend activities scheduled there. From a lake cottage you can easily do day trips to White Mountains. On the Wolfboro side of the lake (the lake is huge) you aren't too far from Portland Maine. A bit more than an hour I think. This makes an easy day trip to Maine or Portsmouth NH. Portsmouth is great for Strawbery Banke Museum, restaurants, boat trips. Get a NH Atlas and Gazetteer at most book stores. This gives detailed road maps plus location of waterfalls, covered bridges, etc. Haven't been to Squam Lakes Science Center in Holderness for many years but that's another idea. Twice we have seen black bears in the Ctr Sandwich area. Visit some apple orchards before you head north. There are several around the Concord NH area. Gould Hill in Hopkinton has a lot of varieties plus a nice view toward the mountains. If you kayak, there are rental places. Friends who live in Wolfboro kayak on a smaller lake. Lake W is too big. Best wishes.