I used to live in Anchor Point (10 years ago now). I camped on the the mouth of the Anchor river for several weeks before I could close on my house. It was remarkable and heavenly - the fish weren't running.
On many of the area rivers quiet camping and fishing do not go together. If you looking for a quiet experience most areas are pretty good as long as the fish aren't legal. Once they are legal you will have every Tom, Dick, and Harry walking through to get to the place they can share "the" spot they need to fish.
My advice: Fish at a different place than you camp if you want any kind of privacy. If you want a party - get there early and lock everything that isn't bolted down.
The regulations are constantly in flux - this is how to best manage the fishery. Pay attention and you won't have any problems - fishing shops are great resources and there's plenty of them.
The peninsula has lots of places to camp and short of July 4th there is usually space (when the fish aren't legal). The closer to Homer the fewer weekenders from Anchorage too. There's always room on the spit in Homer. Have a beer in the Salty Dog while you are there.
Just my $ .02