The fastest route is using I-15 between Las Vegas and San Diego as Midwest Michael wrote above. However, it is going to look like you are driving through LA, because I-15 routes through the greater LA metroplex. If you were wanting to avoid any semblance of LA, you would drive down US-95 and then either take CA-78 (which is a pretty drive in the mountains) or one of the other north/south routes to I-8 and over to San Diego. These routes will add about five hours to the journey.
Once you determine which route you are going to drive, we can give a better idea of fun places to stop and explore on the way.then again between Vegas and San Diego. I plan to break both those trips into two.
Mark