It shouldn’t surprise anyone to learn that Mount Whitney  is a wonderful place to rock climb. You can climb up the steep East Face of the mountain or head up the Needles. These climbs are not beginners’ journeys, but the East Face isn’t the hardest climb ever either.
First climbed by John Muir himself in 1931, most of the East Face rates at a Class 3, with the worst bits rated 5.4.
The Needles are famed among big-wall climbers who attack the Sierras each year.
If you want to make the climb (or even day-hike), apply for a permit in advance and check reservations (Wilderness Permit Office, 760/873-2483, daily 8 a.m.–4:30 p.m.). Also check the National Forest Service website  for information about how to prepare for a Mount Whitney hike.