Most of the lakes that close to Long Beach don't have camping. The ones that do have camping are typically the windier lakes, which isn't the best for 10' inflatables :)

That in mind, I would google around for: Castaic Lagoon, Silverwood, Perris, Big Bear Lake, and Piru. I'm not sure off hand if the pay to fish lakes like Santa Ana River Lakes and Irvine lake have camping so you might check in to those if that type of fishing arrangement works for you. Also take a look at Laguna Niguel, even though it doesn't have camping, it's a nice small lake that's fairly close to you.

-Rob