I am with @69kv and everyone else here. Most of this plan is a pipe dream.
There is no location you can stay where courses are centralized, except maybe mid/north Scottsdale … but the majority of the courses around there will all be well into the $100 range in December. Lodging in that part of town is expensive, as well.
Playing 36 in December is … optimistic at best. The days are short and the courses are full.
Uber is a no-go, and I can’t see how it would reasonably save you money over a rental car anyway.
I’m not sure you’re going to find 4-6 rounds in the neighborhood of $60 in December. I live here so I get resident rates and that’s a tough ask. But, mid-week, you’ll probably be able to find places to play. As others have said. You’re looking at munis (not the best ones, though, Papago, which is a good golf course with nice views is $100+ in season).
GCU is a fine course, but the views are of trees and the tough neighborhood surrounding it. Ken McDonald has you looking at a power station all day long. Aguila might be a good option. Not the best course you’ll ever play, and it’s a bit of a drive from anywhere, but the views are nice for a muni.
If you’re from a northern climate and the idea is just to get somewhere you can play golf in December, cool. Otherwise, be very realistic about what your budget can support. And be aware that (at least in a typical year-though 2020 has been anything but typical) December is among our coolest and wettest (both of those are obviously very relative) months.