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.
If you are willing to allow dirt roads in your definition of "getting away", you can get a hell of a long way from civilization in the western US.
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.
I expect some of these roads haven't seen anyone (person or car) for years.
"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.
The forest service, at least in some of the more "popular" areas in WA, CA and OR sometimes rates the road on their motor vehicle use map so you know the likelihood you'll actually be able to use it. On BLM land I've found map roads that there is little no evidence of at all.
Perhaps it is more "speaking" to give what that distance means in terms of area. A radius of 50 mi. would mean an area of approximately 7854 square mi. Doesn't that sound like a lot now?
In one of the places on this list, quite near the stated "most remote spot", the realization, "Whoa, we are considering bailing off this route because of poor/dangerous conditions, and the shortest bail is about two days' walk." was quite a revelation.
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.
