There are many great rivers on the Island that people can fish. Most of the bigger ones have hatcheries, but only a few have accessibility like the Vedder does, which for most people is the key reason they fish it.
The Stamp river has good fall salmon fishing as well as steelhead opportunites and while I have never fished it, the Gold is probably the same.
Nitinat river produces some of the largest chinook and it is rightfully regulated as well. I have fished this river a couple of times and for its isolation, there is a good presence of undercover and plainclothes officers there to watch for snaggers. Good on 'em in my books.
The Cowichan is probably the most famous island river offering salmon, steelhead and good resident trout fishing. It has a healthy population of self-sustaining brown trout too.
Most of the rivers provide wonderful mouth fishing like the Big Q for Coho and Chinook, or the Oyster for its Pinks, the Campbell and Quinsam system for the Tyee Pool.
There are lots - just grab a map and take a look and most likely you will find a river that offers opportunities. You will need a backroads mapbook to get access to most and a good set of walking feet and adventurous spirit to get to the rest. Enjoy the island.