I like to paddle from either Avalon Harbor or Two Harbors on Catalina Island to the middle of the island near Twin Rocks. That's about 7 miles one way from either launch site. You can rent a decent SOT at either location and, if you want, return it at the other location, allowing you to cover the entire distance between Avalon and Two Harbors - about 14 miles of some of the best coastline in Southern Cal.
In the Twin Rocks area, you can safely land and camp in a number of small coves. Campsites are primitive - a wooden camping table is the only convenience. The fee is very reasonable, about $12 a night. Reservations can be made online here: http://www.visitcatalinaisland.com/twoHarbors/camp_boatIn.php
My favorite campsite, which also happens to have an old unserviced outhouse on the bluff above the beach, is Goat Harbor. The view from the outhouse looks like this:
Not bad, eh?
Here are a few shots of the beach:
In terms of your four-year old, the only real question is whether he can sit in a kayak for 2-3 hours to get to the campsite. Once there, I am sure he'll love it. Lots of smooth rocks, gentle or no surf, places to climb around. I am planning on taking my 6-year old and 9-year old soon. The only problem I have is transportation - I would really need a triple kayak with room to spare for gear. Or I would have to rent two doubles, with my wife and myself each paddling with one child.
Let me know if you want any additional info.