I live in L.A. and am a native. Check http://www.quikbook.com
for hotels - nice aspect is that for most you don't have to pay in advance. You can cancel as long as you stay within the hotel's cancellation policy.
Several worthwhile places mentioned by others are close to each other: Farmers Market (and The Grove), the Los Angeles County Museum of Art, the La Brea Tar Pits, Melrose Avenue (though it is not as interesting as it used to be), a drive through Beverly Hills (Rodeo Drive), the Sunset Strip - though the last two would fit well with a visit to the Getty Museum or the Getty Villa. For the Getty museums, I believe that you'll need to make parking reservations in advance. You'll probably enjoy a visit to the UCLA campus (sculpture garden, inverted fountain, lovely brick buildings) more than Art Center.
If going to Pasadena, see the Norton Simon Museum (terrific collection) as well as the Huntington Library. Wear comfortable shoes, as the Huntington has over 200 acres of beautiful gardens.
I'll be glad to go deeper on this if you have more questions.