Bob Hope Airport and LAX are both around 30 minutes away so which airport you choose to fly to or from LA is fine. I would say LAX might have cheaper fares since they're a bigger airport but I'm not...
For private planes the closest airport is Whiteman (WHP) about 15 minutes to the west. For commercial flights the closest airport is Burbank (BUR), about a 20 minute drive to the southwest.
La Jolla is a suburb of San Diego, CA. Lindburgh Field is the international airport in San Diego, and the closest commercial, big jet field to La Jolla.
The closest airport to Heathrow is RAF Northolt (17 miles away from Heathrow) and the closest commercial airport is Luton (36 miles away from Heathrow). Gatwick is a lot further away (44 miles from...