In case you want to see it all on a map - Pasayten Loop GPX
Once I'd seen pictures of Upper Cathedral Lake, I knew I wanted to visit the Pasayten. We planned a few approach routes, and ultimately decided to start at 30 Mile Trailhead. We set off up the Chewuch trail in the blazing heat (there was a heatwave throughout most of our trip).
The first 6 miles are through a burn, and there are no options to camp until just before the Fire Creek trail comes in (where there's room for at least a few tents). We camped there, and changed our plans. We'd hoped to go up to Windy Peak and Horsetooth Basin, but decided that due to limited water accessibility and the heat in the burn zone (the Windy Peak trail looked to have more burn along it), we'd go up the forested Tungsten Trail instead.
This proved to be a good idea, as the trail was well maintained, stayed mainly under treecover, and was lined by wildflowers. We camped by the Tungsten Mine Cabin, where we found a somewhat maintained outhouse! There's water access if you follow the wellworn social trail from the main cabin southwest (crossing the boundary trail) and then setting out across the somewhat boggy meadow (maybe a 15 minute stroll) to the beautiful little burbling Tungsten Creek.
The next day we followed the Boundary trail over Apex and Cathedral Passes, and got our first incredible views of the North Cascades. We camped near Upper Cathedral Lake, where inquisitive mountain goats came to visit. Turns out they really do lick the urine off rocks...
We spend our fourth day relaxing by the lake, visiting Lower Cathedral Lake (which seemed to be a lot less visited), and trying to summit Cathedral Peak (a bit too sketchy for us without gear).