-- Last Updated: Jul-08-12 12:47 PM EST --
Great place for what you stated. It's fairly big, free of surf, and there's a good plastic map of it by Franko oriented towards paddlers. Lots of ins and outs make it more interesting than, say, just a big round or oval body of water. If there are swells outside the bay, you may feel their effects near the entrance, but other than that you don't have to worry about much more than wind and other boaters.
There are places to get out and eat lunch or use a bathroom or buy an additional snack. A civilized urban venue, yet you may see sea lions and other marine mammals while paddling.
I highly recommend stopping in at Aqua Adventures to buy the map(s), get more info, or to take lessons. They also rent kayaks if you need or want that, plus every Thursday evening there's a social paddle right from the shop.
If you want to camp, Campland on the Bay (private) is right on the water. Might be hard to get a site in summer, but ask if you're interested. You can paddle to Aqua Adventures from it. Just want to warn you it seems to be a party zone, at least on weekends. But it's clean and well-kept.
If you go back to Catalina Island, try paddling at Avalon, too. Beautiful, clear blue-green water with garibaldi all over the place. Snorkeling is great there and at other locations along the island.