The novelty of the old Route 66 isn't for everyone. You'll drive through a lot of dusty, small, old towns that are either now dead or survive only by selling badly faded dreams to tourists in search of the mythic past. Yes, you may make some personal connections along the way, but honestly you can do that almost anywhere, if you know how.
I suggest deciding on a half dozen or so places you'd like to see and planning a route that connects through them. You mentioned hiking.... You could take a route through the Colorado Rockies and Utah's stunning Red Rocks country, visiting national parks such as Rocky Mountain, Arches, Canyonlands, Bryce, Zion, etc. In California, see if your schedule will permit visits to places like Kings Canyon, Sequoia, and Yosemite. Or just drive Route 2 through the Angels Crest, drop down into LA, and finish up your drive along Santa Monica Boulevard until you reach the Pacific -- the literal far end of Route 66.