I agree you don't need to stay as long in either San Francisco or Carlsbad, if you're already staying in San Diego. For Palm Springs, we've stayed in Rancho Mirage at the Rancho Las Palmas. It was beautiful, and had a lazy river/waterslide/pool for kids. There are lots of places to eat nearby too for all budgets.
Personally I wouldn't stay in West Hollywood either....if it was up to me I'd stay in Pasadena and make that my base for a while, as it's pretty easy to get from there to so many places. You can obviously see the main Pasadena attractions such as the gorgeous Huntington Botanic Gardens and art galleries but it's a quick drive down to Santa Monica, or Hollywood, or even somewhere like Long Beach if you're interested in the aquarium or the Queen Mary. You can also take the gold line metro to somewhere like Chinatown, or Olvera Street (right by Union Station), or Little Tokyo.
Hollywood itself I find a bit tacky...I don't think there's much to do there really - I've taken friends on the open top bus tours a few times and that can be fun, but I don't think you'd want to spend too long there.
Have you considered going to places like Laguna Beach, Newport Beach etc? Or up the coast to Santa Barbara? (beautiful there, but the hotels are expensive). If you do stay in Santa Monica then definitely drive up to Malibu - you might even get to see dolphins as you're driving along.
Anza Borrego state park is another very cool place to visit if you're interested in the desert.
Oh and as for museums/galleries - my favourites are the Getty (cool tram ride up there too!), the Getty Villa (but maybe not a must do if you've travelled in Europe), LACMA, and the Norton Simon (Pasadena).