Burney Falls is my favorite campground but we live in the San Francisco bay area so it is a little far for a weekend trip. We tend to go locally to a few really nice campgrounds in the bay area named Samuel P Taylor St. park, China Camp St. park, and Salt Point if you are interested in campfrounds in this area. The first two are as popular as Burney is, so you have to make early reservations to stay in them for weekends.
My favorite campsite at Burney is number 82. It is wonderfully shady. It has been about 5 years since we have been there so the cabins are totally new to us. As are the new bathrooms. And boy some of those bathrooms were getting pretty old and nasty.
Have you ever gone over to the McCloud area to the McCloud river and falls area? That area is beautiful. We love that area too.