The farthest summit from a road is about 6 miles. Kinda made me sad inside. That's how remote you can get from a car.
I have gone on farther trips without crossing a paved road - one being 120 miles that took 6+ days (tough terrain!) by following the crest of an entire mountain range - quite difficult. As the crow flies, that's about 70 miles point to point. If you stretch the theoretical limit between paved roads - encapsulating this entire mountain range, it's about 78 miles. There's about 3 rough 4WD tracks that you can use to cross it - but that's it, in that entire range, any other point across you have to traverse by foot (and there's only a few trails to do so too).
Hope it stays that way.
But again, it's still always <6 miles to where you can drive a car.
I've been to more "remote" places, such as Alaska, with vast Wilderness- but they let you fly planes into there, which seems somewhat like cheating.