We usually contact a campground early in the day after determining where we may stop that evening. Checking map programs (Google, Bing, or Streets and Trips) or Good Sam gives us a radius of where we plan to stop. We can then plan from there.
BTW OLD 66 has pretty much been replaced by interstates. Be careful that you don't get on an old stretch still identified as US66 and find it is not maintained or dead ending somewhere down the road. This is very common on parts of 66 that traverse AZ and NM.
Here is a link to some good info on route 66 through AZ:
Arizona Route 66