One recommendation: Enchantment Lakes in the Alpine Wilderness of Washington.
Late summer (after snow melts) and early fall (larch trees turning color). Heavy use mitigated by permit system. A spectacular area of polished granite, many small crystal clear lakes joined by cascading creek, lots of nooks and crannies for roaming.
Lots of elevation gain to Lower Enchantments (looks like a High Sierra setting, from pictures I've seen of Sierras), then more elevation to Upper Enchantments (desolate but spectacular, too).
Some other descriptions of Enchantments:
Another great trip is traversing North Cascades National Park -- either east to west, or the reverse -- between Hannegan Pass on the west side and Little Beaver Valley (or Big Beaver Valley) to the east where those valleys drain into Ross Lake.
Can arrange for drop-off or pickup by boat at the mouth of either Big Beaver or Little Beaver river, or both if one is used valley is used as entry and the other valley is used for exit from a loop up to Whatcom Pass and back.
Whatcom Pass provides terric views of hanging glaciers on Mt. Challenger (also great views from most of the 50+ switchbacks on the east side of the pass).
Very unlike the Enchantments, both as to scenery (great variety with deep forested river valleys plus very rugged glacier-covered peaks and high passes), and as to crowds. Quite simply, there are no crowds in this area of North Cascade Nat'l Park (at least not in my trips there, with the first about 30 years ago, and most recently about 3 years ago). Might make the whole trip across the park without seeing another person; and if you cross paths with three or more parties over 4-6 days, it's either rush hour, or you're pretty unlucky.
Some descriptions of the Hannegan Pass/Whatcom Pass trail with various options for loops, side trips, and alternative routings (e.g., Cooper Ridge High Route):