One suggestion is the small oceanside town of Marina Del Rey. It is the ideal home base for your LA stay and only four miles from LAX and walking distance to Venice Beach. In addition to proximity, Marina Del Rey also boasts a plethora of water sports and beachside activities to enjoy. Or if you are there to relax and be pampered the town has many picturesque hotels and inns to choose from.
Source: http://www.visitmarinadelrey.com/visit/where-to-stay-in-la