There are lots of New England Fall trip advice is you do a search on Fodors. If you don't want to drive perhaps fly into Boston's Logan airport and take Concord Coach bus to Portsmouth NH. There is also bus service to Portland ME. Then you can Uber around although both are small cities where it's easy to drive around. Both have boat trips you can take. Portsmouth has Strawbery Banke Historic Area. Perhaps consider renting a car for one day to see more scenery.
You could also take the bus to Concord NH where there is beautiful scenery and easy drives. You could visit Gould Hill Apple Orchard in Hopkinton which has a nice view looking toward distant mountains and you can sit outside enjoying a flight on their hard cider. Nearby Warner has a foliage festival also the Kearsarge Indian Museum, Telephone Museum, etc. I do NOT recommend going to the mountains or other tourist magnets where there will be a lot of traffic. If you stayed in Concord, there's a Marriott hotel at Horseshoe Pond where people enjoy walking and there's a good chance to see some wildlife. Carter Hill orchard has an area to view migrating hawks (except I can never remember dates for best viewing). If you had a car and wanted something unusual, Miles Smith Farm runs an air b&b in Loudon NH (next to Concord and only a few miles from Canterbury Shaker Village). They raise Highland cattle at Miles Smith. It's a small farm off on a dirt road. Nice owners. There are also quite a few hiking trails in Concord. If you had a car you could also visit Mt. Kearsarge which has splendid views from the Wilmot side, Winslow State Park.
I could go on and on. Perhaps pick the historic area you'd like to visit and work from there. Manchester NH has a much smaller airport and is easy to get to via car but I don't think it has good bus service. Lately prices have been lower to use Logan. It wouldn't be difficult to rent a car at MHT and drive east to Portsmouth or north to Concord. From Concord you could do an easy day trip to Vermont. Portsmouth is next to Maine and would be my choice if I wanted a lot of seafood. Portland ME has an incredible number of great restaurants. You could get a lobster roll from the Bite Into ME food truck in Fort Williams Park and then enjoy the wonderful view of Casco Bay.

You should definitely rent a car, public transportation in rural New England is minimal, and the driving is easy. You could do the seacoast or the mountains or with 6 days, you could do a little of each. The mountains definitely have more spectacular foliage, but the seacoast is less busy in autumn, and in early autumn you can still enjoy beach weather. Foliage season runs from late Sept to mid Oct - this is the busy season in the mountains. However, there are plenty of quiet back roads (many are gravel) everywhere that you can explore. Dfrostnh gave you some good ideas. There's a lot to see and do in New England, each state has it's own personality. Here's a web site to get a feel for the area - https://newengland.com/

Zootsi, Yankee Magazine is a great recommendation. We're subscribers. There's a lot of great info on their website. thetravellife, glad you checked mileage. New England is very easy to navigate except for places like Boston although Boston has great public transportation.