California has a lot of parks but you can cross two off your list at once by visiting Sequoia and Kings Canyon, just south-east of Yosemite. They are two distinct parks, but are co-managed and share a border and an entrance fee ($5 a head). Both offer lodges and campdsites, but keep in mind that only a very small fraction of these remote and rugged parks are accessible by road. To really see them, you'll need to take a hike.
Sequoia is home to the largest tree in the world, by volume. Redwoods are taller, but giant sequoias win for sheer mass: the General Sherman's trunk has a volume of 1,487 cubic metres and is estimated to weigh over 2,000 tonnes. Sequoia also boasts 4,421m Mount Whitney, the high point of the John Muir Trail, which runs through Sequoia and Kings Canyon on its way up to Yosemite.