You mentioned wanting to be able to talk to locals, learn about culture and enjoy some nature, so for this I think it would be great to spend a couple of days in Nikko and then head to further north. Nikko is right next to Oyama but is surrounded by nature: forests, mountains, valleys, gorges… Two days will be enough to see Nikko’s famous temples as well as discover some of these green areas, maybe try out one of Japan’s famous hot spring if you wish!
The Northern Region is connected to Nikko, the town was in the past the gate all travellers had to pass through to be able to continue north of Tokyo. A few post towns were built along the trail to let travellers stop to rest, and visiting one of these traditional towns is recommended! The trains will then take you well into the region and you’ll be able to see a wide mix of culture. Many traditional activities could be included, such as riding a rickshaw, listening to a shamisen (Japanese instrument similar to a guitar), riding a traditional boat, listening to folk songs, etc. This area is quite rural so the customs remain much stronger here than in Tokyo and other urban areas further south.
Of course, this is just a first draft without knowing much about your group and interests, but if you’d be more interested in other things we could easily change them around.
Here are some photos from my own travels around the area, featuring some sites that could be included in the itinerary:
And of course, trying the different local specialities too!