If I was going for "experiencing California," I thinking I'd vote for Hollywood. The Palm Springs tramway is very nice, but one reason people go up in it is that the area at the top is very different than most of Southern California, at least without serious hiking to get there. Cool and wooded. Great views, though.
Plus it's a long drive out to Palm Springs to do one thing; in Hollywood/LA you could do several activities in the same amount of time. Depending on traffic, Hollywood is less than an hour drive from DLR vs. about two hours out to Palm Springs.
PHXscuba