Airport, Santa Monica
Santa Monica is much better than staying in Burbank or Long Beach - the big question is time vs. money if you have the option to fly into LAX, its much closer. If you can find a bus or shuttle that will get you to SM for less than $50 from Burbank or Long Beach, great, but you may spend hours waiting or trying to navigate your way around. Its really a cost benefit decision, but there's not much worthy in Burbank (unless you want to go to Universal Studios, which is pretty close to there and may be near where Leno films) and SM is a way better beach city than Long Beach...
Jeannie (our host) picked us up there. She drove us all around with her fancy car. So, I sugget you to rent a car, but be careful that you don't stuck on your way.
For exploring city centre just walk, relax, and have fun!