Mammoth, on the north side, is the park headquarters and is like a small village with museum, hotel, old fort, and the campground is on the side of a hill so has several levels with good views of the valley, etc. Not a lot of shade.
Norris is almost in the middle of the park, so well located. Shaded well, small so not too crowded.
Madison is on the west side and very shady with lodgepole pines and on a river. Very popular so it runs full most of the time.
On the east side, Bridge Bay has two sections...one is open with few trees and the other has more trees and shrubs. Close to the lake and Fishing Bridge..hotels, dining, visitor center, etc.
These are the ones I like best. Whichever ones you choose, get reservations NOW or it is likely you won't get what you want when you want it.