Route 66 has been largely replaced by modern superhighways. The process began at least 30 or 40 years ago and has continued until now. For much of the route, old Route 66 is buried under new modern highways or city streets. Some sections of the old road exist as small pieces of road paralleling the newer highways. In places, the local towns and states have restored bits of the road as tourist attractions.
If you want to search out those pieces of the old road, you can purchase a book that gives you detailed descriptions of how to find them. If you are looking for the nostalgic old Route 66 that has been portrayed in films and books, that no longer exists. I have driven on portions of Route 66 and think it is interesting for a short while. After that, I can think of hundreds of attractions in the Southwest that are far more interesting than an old roadway.
Some of the longest intact portions exist in the California Desert and in the Arizona rangelands. If you drive to Kingman Arizona, a few hours south of Las Vegas, you will be at the center of several surviving stretches of Route 66. To the west, there are some long stretches of Route 66 through parts of the Mojave Desest. To the east, a 100 mile arc of the old road that has been bypassed by the new highway goes as far as Seligman. Williams Arizona just south of the Grand Canyon is one of the old towns that was on route 66.