Places to eat in Malibu?

I agree with all of Rachel's selections. Here are a few more:

At  Malibu Country Mart, in addition and  Taverna Tony, you'll also find the Malibu outpost of  Mr Chow - Malibu. 

But If you're visiting Malibu, you'll probably want to eat at a beachside restaurant (at least that's true whenever I go to Malibu). 

So along the Pacific Coast Highway, in addition to Geoffrey's Malibu which is a classic, there's the Malibu outpost of  Nobu Malibu, which is stunning, and the brand new  Nikita Malibu, a Mediterranean / Italian restaurant located right next door (here's a photo). If you're looking for something more casual and not so much of a "scene," there's  Moonshadows Malibu which hangs over a rocky beach. Again on the casual side (and a little touristy) there's  Paradise Cove Cafe where the setting is incredibly beauitufl and the tables outside are directly on the sand. I prefer this place for breakfast or dinner during the week when it's not overrun. 

Have fun in Malibu!

UPDATE: I wanted to add one more place to this answer. I was recently in Malibu and went to Lily's Cafe & Pastries. It's a real "locals only" kind of place hidden in a small outdoor shopping center. They serve awesome burritos (the breakfast burrito is a local legend). Go here for a quick/casual bite before or after the beach. 

Malibu Seafood is the best and freshest, especially if you just want a chill place across from the beach to eat.  It gets super busy and they take phone orders if you don't want to wait in line.  www.malibuseafood.com

There are some great places to eat out there but just to name a few:

Taverna Tony, Geoffrey's Malibu, Malibu Country Mart, and even Malibu Beach Inn are a few of my favorites!

Carbon Beach Club at Malibu Beach Inn! I hesitated to recommend just because it's my favorite secret little spot, but I had to give them (and y'all) some love. Excellent food and service, indoor seating and an outdoor balcony that overlooks the Malibu Pier.

If you're looking for a delicious, cheap bite for lunch, you can't beat the fish tacos at Lily's Cafe & Pastries. Another good option for cheap seafood is Malibu Seafood, where you can BYOB to their picnic tables overlooking the ocean. If you're there on a Sunday and want to make a short drive north, Neptune's Net is a biker bar with awesome fried seafood. I love to go there and watch the surfers just across the highway. If you're looking for somewhere nice for dinner, Geoffrey's Malibu is great and has wonderful views.

All of the above are great suggestions! For breakfast or brunch, there's an ADORABLE little place that recently opened at the end of a pier in Malibu called Malibu Farm Cafe. All the ingredients are SO fresh, and the owner takes a lot of pride in being the chef and menu designer. She is very into the locally-sourced, organic, wholesome food scene. I remember I got the basic breakfast plate of scrambled eggs, toast, and sauteed veggies- but EVERYTHING from the strawberries in the strawberry jam to the herbs in the scramble were so obviously freshly picked that it was DIVINE. My mom got the cauliflour lavash pizza, which I most definitely am getting next time because it was fantastic. Please do go!

I love Paradise Cove Cafe. Perfect lunch spot for a day trip to Paradise Point. This is pretty north into Malibu so it's best to plan to stay a few hours. I highly recommend the Calamari here!

I agree with Malibu Country Mart, too. Great lunch spot right across the street from the beach. They have a playground so if you have kids you can enjoy your lunch on some outside picnic tables while your kids play.

I also love the Reel Inn Restaurant. Hands down some of the best seafood in Malibu. this is another place that can get really crowded on the weekend. One of the first owners of the this restaurant was professional wrestler Fat Jack McGurk!

There's also Moonshadows Malibu which is one of several great restaurants right on the water. a real celebrity hangout and the restaurant mel gibson was leaving when he got pulled over.

Duke's Malibu is always a solid choice. right on the water. great prime rib.

By the way, off Pacific Coast Highway (which is always a beautiful drive) there's a place called johns garden. they have the best sandwiches. and playground out front if you're so excited by your sandwich you need to celebrate by hitting the slide.

The new Nobu is a great spot. The restaurant itself is amazing and the sushi is some of the best in LA. It's pricy but worth it. It's a great spot to go for someones birthday.