Farther afield...

Although I talk most about the Uintas, because that's where I'm going again this year, and because that's the easiest big, dramatically scenic mountain range for me to reach, I should point out that it's not the be all end all of my desired destinations.  Where else would I like to hike, if I had to make a short-list of about 10-12 destinations?

• Although Washington State and the PNW region in general annoys me in many ways, I can't deny that there are phenomenally scenic places to visit.  Sadly, some of them, especially those closest to Seattle, are visited by hordes of granola, outdoorsy types, which means that you either have to deal with crowds, extremely limited permits, or both.  But there's a few places that I think would be worth the trouble:
• Glacier Peak Wilderness
• The Alpine Lakes Wilderness, especially The Enchantments area
• The Goat Rocks Wilderness
• Honorable mentions go to a variety of destinations in the North Cascades National Park and Mount Rainier National Park.  I also know eloquent advocates of the Olympic Range more specifically.

• My annoyance with the PNW is matched by my equal annoyance with California, but you also have to admit that the Sierra Nevadas are not for nothing known as one of the premiere backpacking destinations on the continent.  The John Muir trail, at about 220 miles, is the longest single expedition trail that I'm likely to ever attempt (something like the PCT or the AT is simply too long away from home to appeal to me) but for this list, I've focused on more modest destinations, many of them described by Peter Potterfield in his hiking books.
• The Rae Lakes Loop in King's Canyon National Park, including a hop over to Kearsarge Basin.
• The Yosemite Grand Traverse, a 60-mile epic that you can do after seeing the touristy parts of Yosemite Valley in the park.
• An out-and-back or loop from Devil's Postpile up to Thousand Island Lake and thereabouts.  I'll note that the JMT actually covers much of the same territory that these hikes do.
• Wyoming, on the other hand, is a state I can relate to, and the Greater Yellowstone Ecosystem area has some of the most highly desirable hikes on my bucket list.  Plus, unlike the west coast hikes, I can drive there in two days rather than three.
• The Teton Crest Trail is the top destination here.  That said, it may get a bit crowded relative to some other destinations, such as:
• The Shoal Falls Loop in the Gros Ventre (I'd probably do as a warm-up to Teton Crest.  Both together are little more than a week long.)
• Lots of potential destinations in the Wind Rivers (Titcomb Basin, Cirque of the Towers, Indian Basin), the Absarokas, and the Beartooths that are high on my wish-list.  Not to mention within Yellowstone itself.  And that's just scratching the surface of mountain ranges in the area.  It may be a bit cheating to conflate all of them into a single bullet point for purposes of this list, but honestly, I haven't tried to prioritize them yet.  I want to do them all!
• The Maroon Bells Circuit.  Have to do it.  Would prefer September, with bright yellow aspens, of course!
• Lots to see still in Glacier National Park, although rather than extended backpacking trips, I'm more inclined to see this as day hikes from a base-camp in one of the lodges.  Next time I'm in the area, I want to add Waterton Lakes National Park just over the border in Canada while I'm at it.  I really enjoyed Glacier when I was there a few years ago, but it was a high snow year, I was there too early to even get to Logan Pass (too much snow) and we were only there a few days.  I barely scratched the surface of one of the most beautiful areas of the Rockies.
• I went once to the Chicago Basin in the San Juans in southern Colorado as a teenager, and I have a strong desire to head back to that range.  I know that there are a lot of routes and destinations to choose from, and I haven't really researched much in the way of what I'd want to do yet.
• Coyote Gulch is probably short enough that I could pair it with a trip to Chesler Park, or Fish Canyon nearby.
• Rim to Rim to Rim hike of the Grand Canyon
• Southern Rim hike of Big Bend National Park.  Plus, a bunch of day hikes to places like Grapevine Hills, Santa Elena and Boquillas canyons, etc.
• Speaking of hiking in Texas, next time I visit my folks, I want to time it where I can go backpacking without it being ridiculously hot.  I'd love to see Palo Duro and Caprock Canyons State Parks.
• I'm not that up on what's hot in Canada, but there are a few destinations in Jasper and Banff National Parks (and the other parks nearby) that have caught my interest:
• Skoki Valley
• Tonquin Valley
• The Rockwall Trail in nearby Yoho and Kootenay National Parks.