I drove several sections in New Mexico during the three years that one of my sons lived in Albuquerque. Parts of it are fascinating.
Take advantage of resources like those posted earlier in this thread. Route 66 has attracted many history buffs over the years. There's a lot of information on it out there, not hard to find. You'll find more in the form of free tourist handouts when you get there, but that doesn't help for planning.
As for hiking: a whole separate topic. There are lots of good places for it along the route. Which ones you want depends on the season.