Payson Az. to Newport Ca. best route

100 miles shorter to go through Phoenix.

87-202-10-71-55 is 454 miles
Through Prescott Valley, 260-169-89-40 then on to Newport is 564 miles
Through Flagstaff, 260-Lake Mary Rd-40 then on to Newport is 565 miles

87 south from Payson to Phoenix is very good road. Mostly 4 lane divided almost all downhill. The other routes through Prescott, Camp Verde or Flagstaff involve a climb from Payson (5,000') up to around 7,000' elevation before descending. The roads are all good although some are rather winding and mostly 2 lane.

If entering Phoenix during rush hour it maybe worthwhile to take 87 to Shea Blvd to 101 to 10. This will bypass metro Phoenix although it is a bit further.

40 to 15 to 10 to 91 to 55 straight ahead you run right into it, From that area of Orange County CA .

It's all downhill and it was a good road when I used it. The I-40 from Kingman to Barstow is no prize, I would go the I-10 personally.
Use the 202W loop around Phoenix to the I-10

It's another 75 miles back to Phx. but I was thinking more about the road...

Head back to Phoenix and take the I-10 and save yourself about 100 mi. according to Yahoo maps