Area an hour away from LAX airport

Malibu

Malibu, Mailbu, Malibu. Stunning coastal town with lots of shopping and dining and of course the BEACH! Try Moonshadows Malibu restaurant or Duke's Malibu Duke's is less expensive (but remember this is where a lot of celebs live $$$). Great street tacos and shopping at the Malibu Country Mart. I worked in Malibu for three years and loved it. Everybody is happy and friendly there, a STARK difference from a lot of the rest of Los Angeles. Enjoy in whatever you choose! I love to travel :) 

You might try San Pedro, CA or Long Beach

If you want convenience to the airport, the Inn at Playa del Rey the single hotel in Playa Del Rey, is a quick few minutes drive on surface streets to the entrance to Los Angeles International Airport

It's fine for a night as the beach and several good restaurants like The Tripel Playa Provisions and Bacari PDR are within walking distance of the hotel.

Like others recommended- Manhattan Beach for a quick stay and if you have more time, then Venice near Abbot Kinney.

Given the insane traffic. I would recommend the Venice Beacharea. Stay in Marina Del Rey, you can easily walk to Venice beach. For a quiet stay- marina del Rey hotel. For a closer to Venice stay, the JW Marriott Los Angeles L.A. LIVE  is quiet a scene that you shouldn't miss. Walk the boardwalk for plenty of bars and restaurants. You can get to lax pretty quick on the side streets and avoid the 405.

Definitely Santa Monica or Venice Beach. I love Manhattan Beach as many people have suggested...it's beautiful and very close to the airport, but not exactly a tourist destination. Santa Monica and Venice have much more to see and do, amazing cuisine and shopping. The other beach destinations around LAX have largely pubs and mediocre food. You can also find some really cool boutique hotels so you're not spending a ton of money in either city, but more specifically Venice. Try The Kinney in Venice...it's right by Abbott Kinney which is exactly where I send all my East Coast friends visiting LA for good restaurants and shopping!

You might try San Pedro which is the port for LA

Manhattan Beach is good.  Recommend restaurant - Fishing With Dynamite

Jack Hamlett is right, Manhattan Beach is a good place to stay. I would also recommend Santa Monica , which can be pricey. Long Beach is also a great place to stay, and it's the second largest city in L.A. County. Belmont Pier has an excellent restaurant for seaside dining.

Hi! I highly recommend Hermosa Beach. Right on the beach, plenty of bars/pubs, restaurants, pier and more. Just 30 min or so from Los Angeles International Airport

Just south of airport in Manhattan Beach nice food ,nice pier to go on, great people ,lots of small self owned shops with very neat things to buy. Great food ,if I didn't already say that .

Manhattan Beach15 minutes away to El Porto 20 minutes to downtown by the pier. Hopefully you'll be there for sunset.  Enjoy!

My top vote would absolutely be Manhattan Beach although, if you want to see the rest of the city, you're going to be a little far south. Venice Beach or Santa Monica will put you just that much closer to the rest of the city. It just depends what else you want to see while you're here. 

Try a stay in the South Bay, specifically Hermosa Beach/Redondo Beach. There are lovely beachfront rentals. From there the world is yours, bike ride up the strand, eating at one of many fabulous restaurants, and a village feeling you don't get in any of the beach cities from Malibu to Rancho Palos Verdes, RB is my favorite beach town.