Start out @ Agnew Meadow trailhead & head up to Shadow Lake, Lake Ediza & Iceberg Lake. Then backtrack to the junction going to Thousand Island Lake. Be sure to return to Agnew Meadow from Thousand Island Lake via the "High Trail". The scenery from there is spectacular! Get your permit from the ranger station in Mammoth.
actually, you do not need to backtrack. This is off-trail option: Once at Ediza, follow a use trail going up a little while, then veering off trail to the right to Nydiver Lakes. Once there, pop over Whitebark Pass. Normally class 2, but this year with more snow likely problematic on north side as you drop down to the small lake above Garnet Lake. From there, you can either follow the northern shore of Garnet back to the JMT, or go over Garnet Pass to Thousand Island Lake. From there, return on use trails on north shore of TI to meet established trails to Agnew/Mammoth via either JMT, River Trail, or High Trail/PCT. I'd do the latter choice.
The Whitebark and Garnet Pass options are off-trail. I believe at least part of this was the original route of the JMT years ago.