"I have to agree with those who nominate Blue Canyon and the area around Tunemah Peak as the most remote and also least visited. Coincidentally, just this morning I spoke with Allan Clyde, operator of Clyde Pack Outfit, who runs packtrains in this area. He informed me that the Tehipite fire in 2008 cleared out the brush and blowdown which made the Blue Canyon trail difficult to follow. In addition, the USFS and USPS reworked the trail extensively this year to the point where he can take pack trains far up into Blue Canyon for the first time in a decade. So Blue Canyon is not as remote as it used to be."
Since Blue Canyon has been mentioned a couple of times already, I'll chime in. While it's not my all time favorite Sierra place, it is very nice and remote. The lower part of Blue Canyon has a great view of the turrets and domes in the Gorge of Despair area.
There aren't any "untouched" (Sierra) areas left, as I found fire rings with tin foil in my favorite basin spot, but there are many lightly used areas. I visited Blue Canyon 10 years ago, it was isolated and the trail hard to follow. I started at Wishon, went to Crown Valley, visited Tehipite Dome (where I found a huge cache of food, eyed it hungrily, but left it.) I spent the night on a big rock, then descended to Blue Canyon the next AM. Blue Cyn was very wild, the trail very faint. lots of fallen trees. I tried to locate the Old Tunemah Trail, but don't recall much, so perhaps I did not. I bagged Burnt Mtn, then went over to The White Divide. I bagged Tunemah, got a first ascent of an unclimbed peak, perhaps another, then bagged a couple other's with no names, but which had been previously climbed. The best part of the trip was when I bagged Peak 11,987' "Black Crown Pk" via the w ridge. That peak is about a mile east of Tunemah Lk, which is a beautiful place. I wanted to bag peak 10,234' about a mile from Pk 11,987', but was too tired to descend all that way down. Soooo, as far as I know, peak 10,234 has perhaps never been ascended, I did my homework b4 going out there, and it had no record. I also bagged Blue Canyon Pk. I spent one night at the head of Blue Canyon, totally awesome place, nobody anywhere, if I had had a sweetheart with me I'd have sworn I was in heaven. I bagged Finger Pk and descended Blue Canyon, and near Big Meadow went up to 10,000' Coyote Pass and spent the night. Talk about remote! Nothing there either, no trace of anyone ever crossing it. I spent the night on the ground clutching my Buck 119 as it was heavily forested, and I heard crunching sounds all night long. Anyhow, I tried for a couple of "unclimbed peak possibilites" the next day, nothing was certain (as to whether or not someone had been there before). All in all it was a great trip, I never saw another person, and I was on the move, bagging peaks, and having the time of my life in the most beautiful place on earth. I never made a fire, left zero trash, placed no registers, and left it just as I found it. It really was a wonderful trip.
So yes, I agree that Blue Canyon is pretty remote and solitude is quite possible. All I ask to the people who visit is please, practice minimum impact (leave no trace) etiquette, especially in the timberline country and around the lakes. Thank you.