^
Westwood / Beverly Hills is probably your best bet but if you're going to spend 1 or 2 full days in Disneyland, I would suggest maybe staying at a hotel in that area for a few days, then move to a closer hotel of your choice. I say that because by the end of the day, the drive back to LA from Anaheim is going to be a pain in the ass. And by that, I mean you WILL be stuck on the 5 or the 405 freeways for hours. There are also a lot of amazing dining options near Disneyland. Try going to some of the Vietnamese restaurants in Garden Grove and Westminster. Some of the most amazing Vietnamese food I"ve ever had. If you're feeling adventerous, try The Boiling Crab on Brookhurst in Garden Grove for something fun and different.
Don't forget to give some of the hotels in Venice, El Segundo, and Manhattan Beach a try.
Here's a tip for you when you're going to a Lakers game, Rodeo Drive, Santa Monica etc: Avoid the 405 like the plague during rush hour. If you must, take Sepulveda or La Cienega Blvd. They run parallel to the 405 and it's local traffic, but you will at least NOT be stuck in that mess of a gridlock!
Here's an alternative option: Try
www.airbnb.com. I've used it several times and it works out well for situations like yours.