You can descend from the saddle between the two peaks to the west fork of Hague Creek. This is a bit tricky at first; slow going if you're careful. You can follow the drainage down past a series of unnamed, but extremely scenic lakes. You will eventually go below treeline, at which time the going will get extremely rough; when you get to the fork in Hague Creek, you can follow it up, and follow the drainage to The Saddle. Note the stunning cliffs on the back of Hagues Peak.
This is an arduous, but unbelievably scenic route through one of the wilder areas of the park. Just remember to watch the weather and budget plenty of time-- your exit over the Saddle is well above treeline.
Other possibilities from the Desolations include continuing on to Flatiron Mountain, or returning by following treeline above Chapin Creek. If you return this way, you'll want to stay at or just above treeline; the further down you go, the rougher the going gets.
Hey there. Reading through this site, I happened upon a very minor gramatical/spelling issue I wanted to bring to your attention as a courtesy.
This is a wonderful mountain in one of the most beautiful area of the National Park (aren't they all!!).
I think you meant to make the word "area" plural: "areas".
Thanks! Fixed it!