Teton Crest Trail-Sunset lake or the Basin Lakes?

Don't know about a Mirror Lake, but there are clumps of trees near Sunset Lake, and clumps of trees scattered around the lakes in Alaska Basin. I don't use a hammock, but trees exist in both locations.

For a picture looking down into Alaska Basin (taken from the Teton trail, just past Meek Pass, traveling toward the steep Sheep Steps from south to north, leading into the Basin), see one of the photos at my posting in the following thread —

http://www.backpackinglight.com/cgi-bin/backpackinglight/forums/thread_display.html?forum_thread_id=25181

See the trees down there?

As for the location of Sunset Lake, it's about half-way between Alaska Basin and Hurricane Pass. If traveling the Crest Trail from south to north, you reach Sunset Lake by going down the trail shown in the photo of Alaska Basin mentioned above, then cross Alaska Basin to reach switchbacks that go up the other side of the Basin (you can see that other side in the above photo), and then a short walk (mile or so) to reach (and drop down to) Sunset Lake.

From Sunset Lake, the trail continues north on switchbacks up to Hurricane Pass and then down the South Fork Cascade Canyon to where the trial branches to the right (to Jenny Lake) or straight ahead (to Solitude Lake and up over Paintbrush Divide to exit at the trailhead at either Leigh Lake Trailhead or String Lake).

Just did a Google on Mirror Lake on Teton Crest Trail and found this link to a Backpacker thread that describes Mirror Lake as located in the Alaska Basin —

http://forums.backpacker.com/cgi-bin/forums/ikonboard.cgi?act=Print;f=623107219;t=9991135070

and also found this link to a 2012 Teton Crest trip report with the first two nights spent camping at Mirror Lake in the Alaska Basin —

http://forums.backpacker.com/cgi-bin/forums/ikonboard.cgi?act=Print;f=623107219;t=9991135070