If you have an extra day in Sequoia National Park, then a trip to the Mineral King Valley in the southern part of the park is definitely WORTH IT. It is a beautiful area that really shows off the beauty of the Sierra Nevadas (and I've been to the Alps, Andes and Rockies all in the last year!). If you do go, it would not be worth it to not hike one of the many trails, especially to one the pristine mountain lakes. Me and my friends did the hike to Eagle Lake and it was awesome. So much diversity: streams, forests, meadows, painted mountains, jagged cliffs and a clear blue lake. The road is narrow to the valley, but I thought it was actually fun and only took about an hour and 10 minutes, but don't worry it will be worth the adventure!
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