We have a room block at the Anza Hotel in Calabasas, which is about a 15 minute drive from the venue. This is a convenient option if you are coming to LA just for the wedding. They also can add nights on either end if you want to extend your stay at the same rate. For the extension, you will have to call the hotel.
They have a choice of rooms, with the premium rooms having a nicer view and away from the street. The hotel will be much closer to Burbank airport if you are able to find a flight there instead of LAX.
At 20-30 minutes from LAX airport, this hotel is in the heart of Santa Monica, and a good option to be not too far from the wedding venue while touring LA's beachy westside.
You'll be minutes from the ocean, restaurants, and other tourist attractions that would make your journey a little more of a vacation. You would be a 30-45 minute drive from the wedding venue.
This hotel is a bit closer to the venue with good prices.
Other neighborhoods close to the LAX airport to consider would be Marina Del Rey and Culver City. We're happy to give any advice if you need different options!