Phoenix is a majot city and travel can be difficult at certain times of the day. There are many RV parks located around the edge of the city that fill up quickly in the winter months. You should have no problem finding one in the time period you are looking for. I would suggest looking for something close to the area you choose to visit.
There is little or nothing located between Phoenix and Payson. It's an hour and one half of great views and little more. The city of Payson has several parks that would suit your needs. I mostly camp "on the rim" with no hookups, not what you are really looing for.
Another area that might work would be the Verde Valley. It would put you about an hour from each of the two areas. The weater sould be warm 80 - 50 in mid October.
Wally Byam Airstream Club 7513