I've RV road-tripped old 66, sections of it in Missouri, Kansas, Oklahoma, Texas and New Mexico, the Oklahoma - Texas section twice. I've traveled other parts by other than RV, and since I need to use some parts of the route to get from here to there, there are sections I've used maybe hundreds of times over 35 years of living here. Home is Michigan, Route 66 through Missouri and Illinois is a major part of one of tmy shorter routes back and forth.
There were different alignments over the years, some of the original sections were bypassed, then the bypasses bypassed, before US-66 was decommissioned. Urban routings in particular were frequently changed. Some of old 66 sits under the Interstate highway system, in other places 66 is nearly parallel, still others one or more of the old routes may be 30 miles or further from the Interstate that replaced 66.
So if you want to do this, you need a good book. The best I've found for finding various old parts (not just the final route) is "The EZ66 Guide for Travelers" by Jerry McClanahan, published by the National Historic Route 66 Federation.
Jamie Jensen's "Road Trip USA" gives you a Route 66 trip (along with several others on the numbered US highways) that follows the 1950s-60s route where it is interesting, uses the Interstate where that is more useful (do you really want to spend 4-6 hours crossing Los Angeles or Chicago on surface streets?) and directs you to the major points of interest for each road trip. The link above looks like "Road Trip USA" is now available as an web resource; I like the book for bedtime reading.