Seven small backpacking sites are tucked into a hillside at the east end of Sunol. The sites are much prized in the springtime, so you'll probably have to reserve one months in advance for weekend outings (weekdays have much greater availability).
Note the four-mile hike to the camp ends with a very steep ascent to the backpack area; it's harder than you might suspect if you're carrying a full pack.
Backpacking fee is $5 per night, per person. Call 1-888-327-2757 (press option 2, then 1) to reserve a site.