I haven't hiked around June Lake, but the maps show trails climbing to the west from Silver Lake or near Silver Lake. The colors in the area should be stunning -- I was there several years ago in mid-October.
There is a trail to Fern Lake, to about 9,000', that might take you above the valley high enough to view the groves of yellow aspen. A more ambitious trail takes you up to Agnew and Gem lakes. ...or Spooky Meadow -- fitting for October

Check them out (don't forget your camera), and do report back!
Here's a link to the map:
June Lakes map