I was up there twice this year. You want to stay if you fit at Quaken Aspen Camp ground, this is all reserved, but they hold five sites back over the weekend that they let of go late into Friday or so. The camp host needs to like you first, so not one I would depend on. Nice campground with water and pit toilets that are well maintained. Plan B is Peppermint Campground. This is no longer a maintained campground but still has about 5 or 6 sites you can use. Most of this very large campground has been shut down, and being redeveloped very slowly. No running water and no toilets anymore. Here you have a medium hike/walk to the river, but you need to filter this water. I would not recommend Camp Nelson toward the bottom of the mountain. There are also one or two camp sites up by Trail of the 100 Giants. Those tend to be a zoo of people with lots of extra traffic for the Giant Sequias that is about across the street from this campgrounds. When are you planning on going? There might be another option. There are a lot of forest service roads in this area, but I don't know them well enough to guide you anything, and they tend to have marginal maintenance. Quaken Aspen and Peppermint are a short drive to the Giant Sequias. From Peppermint where you always find parking a short hike to the river and then you can hike along the edge for miles. Lots of places to fish, but it takes a hike to get to these. There are more options on the other side of the mountain down towards Kernville. Most of these are not desirable, most without shade and no longer in the big trees. Do not depend on gas within the park boundries. Now this is just one part of Sequia and Kings Canyon National Park and Forrest. Others here should be able to provide additional info.
