Himuro Handmade Soba Restaurant (手打ちそば処ひむろ) is a great place to stop for lunch, featuring cold and hot versions of the noodles, along with some top-notch tempura mountain vegetables like wasabi leaves. Himuro is a rare kind of restaurant that has very carefully considered decorations and style, but also reasonable prices.
Also try hitting up the massive Iwa Shrine (伊和神社), a complex that, with its location far away from the tourist magnets of Tokyo’s Meiji or Kyoto’s Kyoto’s Heian Shrine Complexes, offers serene Shintō scenery.
Kunimi Forest Park (国見の森公園) also has beautiful views (especially during the cherry blossom season) that you can enjoy with a leisurely ride on a special monorail. The sightseeing monorail looks like a rollercoaster that wraps around the forest and hills, ascending hundreds of meters. Of course, it runs at slow speeds, allowing people of all ages to take in the nature views while keeping their lunch (though rollercoaster speeds would of course be fun too….).