Arizona... Seligman for lunch at the Road Kill Cafe....great food and interesting ambiance.....Holbrook AZ..wigwam motel of CARS fame....
Largest segment is in Oklahoma with over 400 miles. See the Blue Whale, and the Totem Pole park.
Do a google search and write to every state that the Mother Road runs through. Each State has tons of stuff to view before you get there.
A word of caution though, with the Interstates following parts of Route 66 we found a couple sections where we followed the Mother Road only to find the road simply ended and we had to back track. I don't know why the engineers couldn't have simply put in an on ramp where the road terminates....Dennis