In reply to kenr:
Correction -- actually it's fairly obvious to avoid Bishop if Tioga Pass is closed. Tho it depends on how bad you want to get there ... could drive north from Yosemite to Carson Pass or rt 50, then south down along the Eastside Sierra on rt 395 (surely more spectacular than driving down the west side).
If someone in your party happens to be into high-mountain free-solo climbing, might want to consider the NorthEast ridge of Bear Creek Spire (4181 meters) - not more than an hours drive from Bishop in the Rock Creek valley. Traditionally side to be "class 4", but the recent McNamara eays it's hard to find a way to avoid a few "class 5" moves.
An easier free-solo alternative might be the East ridge of Mt Russell (4294m) - but that requires a _long_ approach up North Fork Lone Pine Creek -- and almost two-hour drive from Bishop.
. (Up by Tuolumne Meadows + Tioga Pass are a couple of harder and more famous high free-solo routes.)
Mt Whitney (4419m) is the highest summit in the lower 48 states -- and the East face of the Mt Whitney group is about the most spectacular alpine rock wall in the USA - (Trailhead almost two-hour drive from Bishop). But to do a technical climbing route on it is pretty tough without an overnight permit and equipment to make a high camp.
Ken