Two areas that I recommend from personal experience:
(1) Enchantment Lakes Wilderness in the Cashmere Crags near Leavenworth, Washington. From the Snow Lakes trailhead, it's about 20 miles roundtrip to the Lower Enchantments, and another few miles further to the Upper Enchantments. In my first trip, I took two days to reach the Lower, spent a couple days there roaming around, and then one day to hike all the way out to the trailhead. On my second trip, again took two days to reach the Lower, roamed a couple of days in the Lower and the Upper, and then two days hiking out to the trailhead (camped at Snow Lakes on the way out).
Elevation gain from the trailhead to the Lower Enchantment Lakes at about 7000 feet is about 5400 feet.
Here's a link with more details and some trip reports:
Google "Enchantment Lakes Washington" for many more links.
(2) My second recommendation is a traverse of the North Cascades National Park from east to west for about 50 or miles or so, maybe more or maybe a bit less - depending on options you might elect. The east to west version is generally as follows:
Start hiking at the landing at Little Beaver Creek on Ross Lake (get a boat ride from the Ross Lake Resort, where you leave a car);
hike up Little Beaver Creek Valley to the end -- where you cross Whatcom Pass (50+ switchbacks with tremendous views);
then down the other side of Whatcom Pass to the Chilliwack River Valley;
turn right at the Chilliwack River til you can cross it and then follow switchbacks to the crest of Copper Ridge, and follow Copper Ridge generally southwesterly until it takes you to Hannegan Pass;
then go over Hannegan Pass and follow Ruth Creek to the trailhead on the west end of the traverse -- where you have hopefully arranged for some means of transportation to be waiting so you can get back to Ross Lake Resort (if you left your car there, that is).
An alternative to the above traverse is a quasi-loop that is also about 50 miles -- with no need to have a shuttle arranged since you return to where you left your car. As with the traverse, start by taking the boat ride up to the landing at Little Beaver Creek, hike up Little Beaver Creek and then up over Whatcom Pass, with a camp perhaps at a lake above that pass (Tapto Lake) or a few miles west of the pass, then return back over Whatcom Pass and down the other side to Stillwell Camp, then up over Beaver Pass and follow Big Beaver Creek to Big Beaver Creek landing on Ross Lake where (as you hopefully have prearranged) a boat will pick you up and return you to your car at the Resort.
Here's a link to a trip report for the west half of the traverse, starting from the trailhead for Hannegan Pass, going east to Whatcom Pass, and returning back to Hannegan:
And here's a link to a trip report for the full traverse, east to west as I described above, from the Little Beaver Creek landing on Ross Lake to the Hannegan trailhead, and with terrific photos and excellent description:
Finally, here's a link to a site with a lot of info for various approaches and trailheads in the area, including the Little Beaver and Big Beaver routes to Whatcom Pass, as well as info/link for the Ross Lake Resort and boat:
I haven't done the entire traverse in one trip, but have done the Little Beaver-Whatcom Pass-Big Beaver loop and, on a different trip went from Hannegan trailhead almost to Whatcom Pass and then back out (but not the Copper Ridge).
The Olympics also have great trails as noted by an earlier posting -- but I haven't yet journeyed into that area.