Commuting in LA is generally a pain because of traffic at any given time of day. I didn't take the cab much since I lived there, but I know a cab ride from LAX to Downtown LA is a set rate at ~$50. Santa Monica and Downtown LA are on opposite sides of LA with Beverly Hills in the middle. Downtown might be a good choice is you want to be able to hop onto the freeway to any destination quickly. But if prefer a more scenic environment, Santa Monica is beautiful--the beach is right there!
Great for brunch!
A great place to spend the afternoon if you enjoy shopping and prefer to be outdoors.