1

Depends whether you mean a continuous 2-3 week backpack, or if you want to break it up into several shorter trip. The Sierra Nevada in California, which includes Yosemite and Kings Canyon-Sequoia national parks, but also numerous incredibly beautiful National Forest Wilderness areas, all linked together, has numerous options for long trips that keep you up high and not just in the forest. Of course the John Muir Trail is the best known, but there is also the High Route, or you could do a section of the Pacific Crest Trail. Or, consulting with maps and hiking books, you could put together numerous other excellent long trips.
One thing: although the summers in the Sierra are generally quite dry, there will still be quite a bit of lingering winter snow left in June, so high elevation routes may be impassible. July is a better month for backpacking, though mosquitos can be plentiful. It depends on what sort of snow season California gets. If you do go in June, one nice 40 mile loop that is generally passable that early is "The Grand Canyon of the Tuolomne" in Yosemite. Superb deep canyon with lots of waterfalls and sculpted granite.
happy trails

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Check those slot canyons in Utah- starting with Zion National Park (hit the Zion Narrows, Subway), then go check the Coral Pinks Sand Dunes, then Bryce Canyons, then Capitol Reef National Park.

Zion National Park is only 3 hours drive, North of Las Vegas.

You need to rent a car to go to these places. The sceneries are mind blowing. Just different.
May want to do some canyoneering also....