Kings Canyon National Park and Sequoia National Park adjoin each other and are basically managed as one national park. They were established to protect giant sequoia trees (though apparently there is a grove of sequoias in Yosemite as well). The parks are located in the mountains just east of Fresno. The drive up to the Kings Canyon entrance (which would be the north entrance) is a fairly smooth and gradual highway up the mountain (which passes by Project Survival's Cat Haven if you want to see big cats in a zoo type setting). The drive up to the Sequoia entrance (which would be the south entrance) is extremely narrow and steep with hairpin turns for about an hour. Unless you are driving a Porsche, it is not very enjoyable, but it can be done if that is more on your way.
Here are a couple wildlife photos from my trip this summer, taken with a 70-200 to show you how close you can get (these are uncropped and unadjusted except for downsizing). First is a mountain quail and second is a mule deer.