Right on the waters edge, the rock at Point Dume offers a number of great routes for the beginner to intermediate climber. Also not to bad of a view once you get to the top!
There are a couple of different ways to get to the rock, but the easiest will be at the end of Westward Beach Rd. The rock is impossible to miss as you drive further down the beach. Once parked, which I believe you have to pay for beyond a certain point, it's a short walk out on the sand to the base of the cliff.
Make sure you bring all your own gear as this is an outdoor route, though there could be local shops or groups that offer lessons and or rentals nearby but I wouldn't count on it. There are a number of different routes both on the ocean side and the beach side. The difficulty ranges from 5.1 to 5.9. A few bolted anchors can be found at the summit as well as bolts along many of the routes. This place can get pretty crowded on the weekends being that it is still Malibu, but everyone is very respectful.
Whether you want to climb or hang out on the beach below, this is a great spot to spend an afternoon with your friends and family.