Malibu - it's definitely worth a short drive (about an hour) up the Pacific Coast Highway (PCH) to Malibu. Eat at Neptune's Net - make sure to choose carefully between the steamed section or the fried section, as each produces amazing food. Spend the afternoon on the beach.
Venice - explore Abbot Kinney Blvd in Venice. Gjelina for lunch, and The Tasting Kitchen for dinner. Great shops and awesome sea breezes make for a fun day out.
Venice Beach - I did not like Venice Beach at all. It was gross. Like crazy busy, kinda run down, lots of tourist crap. But I guess yes, it is worth seeing once. The skatepark was pretty cool, the beach was pretty perfect, and there's lots of crazies to look at. Also, take a walk around the Venice canals.
Catalina Island - I've never been, but still hope to. A short ferry ride out into the Pacific Ocean.
Palm Springs - two hours inland from Los Angeles. Stay at the Ace Hotel. Prepare to be hotter than you've ever been in your life, lay out by the pool, order the Desert Facial (a cocktail), and enjoy. We love it here!
Death Valley - five hours north east of LA, and one of my favourite places in America. It's just you, the desert, and nothing else. I love this place! The first weekend of November hosts the annual '49ers weekend - celebrating the first people to cross - and get horribly lost in - Death Valley. You'll awake in the morning to the soft sounds of banjos and real country music playing outside your hotel room, and get to watch Dress-Up competitions and dog shows that look like they should be in a movie. But in real life.
San Francisco - totally worth visiting, a truly beautiful city! Friggin windy though, definitely pack the parka! Hire a bike and ride across that gigantic red bridge - the quaint little town that awaits you with the promise of lunch and ice-cream, and a ferry ride home, makes it all worthwhile.
Oxnard - about an hour north of LA. The most beautiful beaches.
Ojai - LA's slightly-lesser-known playground. Stay at the Ojai Valley Spa for a somewhat pricey, but totally worth it, weekend away from LA.
Big Bear Lake - we hit this up for a day trip last summer when my brother was visiting from SA. It was a quaint, little town, with beautiful wood cabins scattered throughout the forest. I believe the best time to visit is in winter, when it actually snows!
Also, you can see my other guides here: Silver Lake, Hollywood, Downtown, LA & Surrounds, and Tourist-ville.