Well it depends on _which_ birthday of course. Knees at 20 are not the same as knees at 60.
Here in the West, Some long hikes include the Wonderland Trail around Mt Rainier (93 miles with incessent elevation changes), the PCT of course, and the John Muir Trail, but i don't think you'll get the JMT done in a week. Based on your timeframe, the Wonderland Trail would be a good shot, but it does require reservations. There is a lottery system in place.
If you really want to get lost in the wilderness, The Frank Church / River of No Return Wilderness in Idaho is huge.
Glacier National Bark / Banff would be an amazing option if you're okay with Grizzly bears.
My local favorite though actually be the little talked about Wallowa mountains in Oregon. You could easily spend a week or two in and around the area. Lots of 9-10k peaks to climb.
Read my review with lots of pictures.
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