This past fall I hit one of the first pushes of fresh kings and cohos in early September, and it was extremely pleasant. There is lots of solitude during the first two weeks of September. Anything after Sept. 15 becomes very to extremely crowded, and in some cases, unfishable in a lot of places. The first week of October through Columbus Day weekend is the hayday of the salmon run. I've also experienced pleasant fishing after Oct. 15. Then the steelhead are targeted. With migratory fish, and taking into account conditions of water levels, temp, etc, these time periods shift I'm sure.
I highly recommend an early run if you can. Avoid the third week of Sept. through the second week of Oct. That is, if you want to avoid the crowds.