I found a great place in Sequoia National Park, not really a campground per se, however a place that you are allowed to park, with no payment, no water, no dump station within 15 miles. Very quiet, lots of deer, huge trees, birds, and at 6,500' elevation, free air conditioning in the summer!
It is about 10 miles south of Hume Lake, where you can buy gas or groceries. Sadly I have not been there since July 9, 2005.
Yosemite Valley is also wonderful. No electricity, lots of trees, plenty of cliffs to look at. Reservations are extremely difficult. Seems like the automated computer system sells out all the sites in about 90 seconds after they open the next month's reservations.
Are you looking for full hookup places, or places that the site is more than 300' square? Well many places that I have stayed, I never measured the miles to the next RV. North Rim of the Grand Canyon is like that. After dark, I could not see another vehicle, only the stars. And nobody around to collect a fee. Camping in the National Forest is fine and free, however camping is not allowed within the National Park except within the 1 North rim campground, or the 6 or so South Rim campgrounds.
Have fun exploring them all!
Fred.