Your main objective could be anywhere, just don't plan on going into casinos or bars. I prefer San Diego to LA as a tourist destination. You can always day trip it up to LA from SD, it's only a couple hours each way, traffic permitting.

You will need 2 stops between Memphis and San Diego. Unfortunately, the exact 1/3 and 2/3 points are out in the middle of nowhere if you take I-40. Probably the most logical stops would be Amarillo and Flagstaff. If you took the southern route - 40 to 30 to 20 to 10 to 8 - you could spend one night in the Dallas-Fort Worth area and the other in El Paso. I am NOT recommending this, but in El Paso, you could walk across the bridge into Mexico. I think it would be a lot safer going a bit farther and spending the night in Las Cruces.