Coyote Flats area just SW of Bishop is a wonderful area to explore!
There is road west of town that runs up a rather adventurous climb to the first flats,, then Coyote is beyond that. We ended up on the broad flats on 10,000 ft, there is a primitive camping area under the trees at 37° 10.564'N, 118° 26.902'W. Absolutely gorgeous spot, mountain cool, with the Pinnacles as backdrop. A cabin and some rock garden trails lie on the branch to the west. I understand the trail southward has been wiped out to all but ATV/bike access; even though it remains in the Mitchell guide books. If you are more adventurous, there is the east facing on trails accessible from the same flats. Or you could go up higher to Coyote. Some images from my trip there last August -
http://picasaweb.google.com/KF6VOM/CoyoteValley2007
I have been looking at a repeat trip that way later in August. I trailed with a few other guys (some in the pix) who went out to nowhere Nevada to watch the Vegas-Reno offroad race first; we trailed the White Mountains and camped at Coyote, the images you see here. I may have a few others if you were looking at cobbling up a group to run 395-area trails.
added -
Also did Wyman and Silver on the east side of Bishop, as described above. Both are nice adventures, but not difficult. A bit domestic especially as you get on top. Much prefer the west side. Pix for those trails -
http://picasaweb.google.com/KF6VOM/WhiteMountains2007