I actually find this rather upsetting. I'd always assumed if you went to the right places out west, you'd be able to get at least 50 miles or so from anything if you wanted to. It seems the west isn't quite as wild as I wanted it to be.
A few places come to mind:
The Deep Creek Range of western Utah (simply stunning)
The North Rim of the Grand Canyon SSE of Hurricane, Utah. Not the popular tourist areas but the extremely remote canyon rim around SB Point.
The Toiyabe and Monitor Ranges of Central Nevada. Pick any valley in the Range-and-Basin country, drive halfway down it, and then head east or west into the mountains.
The Owyhee Desert. Google for Crutcher's Crossing.
The Henry Mountains of south-central Utah.
The Magruder Corridor of Northern Idaho.
"Roads" don't really seem to die. Once they are mapped, they show up forevermore -- even if no-one is taking them and no-one is checking that they are still navigable.
Which can be a startling and frustrating experience in a bad, or even a good, situation...
When terrain and conditions are challenging enough, a few miles' distance might as well be the distance to the moon, when it comes to isolation.
If that notion pulls at you, follow it, but take small and reversible steps.