re: What is the best place to mule deer hunt in the US

It's not that easy unless you have a pile of money. Big mule deer are one of the most valued trophies in North America and the increase in predators and people in the west has hurt.
Arizona Strip is best. You won't draw. You won't draw the best Colorado units for years. If you have the money pile, here is the plan;

Mexico in January. Best pay to hunt there is.
Landowner tags for the Eastern Colorado Plains will turn up a giant.

I will say, an average mule deer looks huge to a whitetail hunter.

Also, major snow this year has resulted in a high winter kill in western Colorado and western Wyoming.

Look up Don Lemon.