If you start in Long Beach would could ride along the coast (part of it on the Pacific Coast Highway) until you get to the Santa Ana River Trail. The river trail will take you to Corona. From there you travel city streets into Riverside and San Bernardino. You can parallel the 215 through San Bernardino. You'll come to a small town called Devore. Go through this small town and you'll wind up on Cajon Blvd. This will keep you off the 15. You do have to get on the 15 for about a mile then you get off at the 138 and go a little east to Summit Valley road. This will take you into Victorville. You can avoid the 15 to Barstow if you take the National Trails Highway (old route 66). To avoid traveling on the freeway you take a few surface streets that take you through Daggett and upto Yermo. Yermo road parallels the 15 for quite a few miles. Then you'll have to get on the 15. Once you get to Jean you get off the freeway and follow Las Vegas Blvd into Las Vegas.
Don't know much about the route through AZ. Take a look as the discussion board on route 66. I do know that some of 66 no longer exists so you'll have to get on I40.