Do you have off-trail experience? Or are you looking for something on trail?
The "no human interaction" part is a big challenge to find in the Sierra unless you plan to go off-trail the whole time.
I can think of so many places in the Sierra that I'd put onto the "Must Do Sometime" list before North Rim in Yosemite. Anything in proximity to Yosemite Valley is best done as a long day-hike, with no illusions that you will get solitude. It's a good early-season project (late June or early July some year), when the waterfalls are all roaring.
The Red Peak Pass suggestion is a great one, much fewer people than is typical for Yosemite trails. However, you WILL have "human interaction."
I think of the northern Sierra (Yosemite and north) as gentle and charming, with slabby granite campsites abutting nice swimming lakes. If you prefer dramatic and vertical, the southern "high" Sierra might be more your style. Nothing beats the backcountry in Sequoia/Kings Canyon Nat'l Parks (SEKI). However, the SEKI does not provide all that much more solitude than Yosemite if you are sticking to trails.
For your combo of "spectacular" and "solitude" and "late August," your best bet is probably a high-elevation area (10,000+ feet) of the High Sierra, either off-trail in SEKI or on-trail in the John Muir or Ansel Adams Wilderness (between Yosemite and SEKI). Be willing to do a longer drive than you might have wished. Desolation Wilderness in Tahoe is only 3.5 hours from the Bay Area, but in late August I can't stand to go there or to the other "short drive" destinations because the higher elevation areas of the Southern Sierra have opened up and there is simply no compare. It is worth the 5-7 hour drive.
I'd suggest investing in the book, "Trekking California." That author has TERRIFIC taste for choosing what are really the most spectacular trips in the Sierra. His trips will kick your butt, though.
Meanwhile, the above-mentioned Desolation Wilderness, as well as other northern Sierra destinations on backpackthesierra.com, are great RIGHT NOW. Get up there even if all you have time for is a short weekender!