Sequoia & Kings Canyon NP/Lodgepole sites 24 & 110
We have lodgepole sites 24 and 110 in August. Fam of 4, tent only. Like privacy, quiet, close to river. Nice to be away from crouds & rv's. See that 110 is rocky & cramped, but is it maybe nicer than 24 for our purposes?
In looking at the map for the campground, neither 24 nor 110 are really that close to the river. You're going to have to cross the road to get to it.
Having said that, I think 24 is going to have more people around you, but 110 is a little uphill and rocky. It's hard to think which one I'd prefer for myself. However, since you said that you would rather have a little bit more privacy, I would pick 110 over 24. Campsite 24 is in the middle of a bunch of other sites, and definitely is set up for RV parking. 110 will give you a more natural environment.
Regardless, you're going to be in a beautiful area. Keep in mind that the 2nd week of August will have a lot of shooting stars, so you should still see some while you're there.
Hope that helps a bit. Have a great time!!
(sorry if this came to you late... I just got a notice today in my email that you had asked a question.)