There are hundreds of places to visit, depending on what interests you. What interests me may not interest you. I travel numbered US highways to stop at places most travelers are quite happy to bypass. What I find interesting are historical connections, places connecting to evolution of our way of life.
The classic guide is "Route 66" by Michael Wallis, emphasis on places Wallis finds interesting and why they are interesting (again, usually cultural history). He also has a Lincoln Highway book, reading that one just now.
For a bit of detail about what is where and how to finding, rather than why you might want to see it, Jamie Jensen covers Route 66 as one of the trips in "Road Trip USA" which also stays on me nightstand for reading.
If you want to follow the road, and actually find the places you've decided might be interesting, a good guide is "EZ66 Guide for Travelers" by Jerry McClanahan, published by the National Historic Route 66 Federation.
I've traveled most of 66 from western Arizona to southwestern Missouri, some sections dozens of times, some hundreds of times. I've traveled other short sections in Missouri (where there are other old routes I like better, like 54 and 36), and longer sections through Illinois, but not all the way into Chicago.
Traveling these older routes I like the museums, accommodations from the 40s through 60s, and finding old bridges and remnants of old road sections. It can take me three days to cover 200 miles of 66 in Oklahoma, when I'm in an exploring mood. Which means, on the average, about six places to see per 100 miles. US-66 in Kansas keeps motor clubs and bike clubs busy for weekends at a time, all 14 miles of it from Baxter Springs to Galena.
I'm not going to write you a guide to all these places, you can buy one and figure what places interest you. Or you can wade through the web sites of the several national associations for Route 66, and the state associations for each of the seven states the route passes through.
I can specifically recommend the Meteor Crater in Arizona. One needs to look at the thing simply for perspective. When one of those things (still flying around out there in collision paths) lands in your back yard, you no longer need fret the other things that might have been worrying you.