I did a little research on this before a recent trip to California. Santa Catalina Island and Anacapa Island were both relatively popular camping destinations. In fact, you can get camping packages that will take you, a kayak and the incredible amounts of water that you will need and drop you off at a camping spot. You can paddle to various other spots from there. Also, Catalina has two small towns, so you can re-supply if necessary (i.e. it probably the cushiest destination).
If I remember correctly, the other islands in the Channel Islands marine sanctuary permit camping, but it gets tougher and tougher as you go farther out (the islands are, in order, Anacapa, Santa Cruz, Santa Rosa and San Miguel). For example, I think that I remember reading that Santa Rosa and San Miguel are completely devoid of fresh water sources.
Santa Barbara island, a relatively small island that is separate from the other islands in the group, also allows camping. However, it seems oriented towards the really hard core wilderness folks.
Fires are generally prohibited and I know from personal experience that the local wildlife are expert thieves (and fond of burritos, I might add). The reason that I mention these two facts is that it has an impact on selecting provisions for the trip.
Good luck!