I hate to be disparaging about anything American as generally speaking Americans take criticism very very badly, but I'm going to. Domestic flights in America are ridiculously expensive and just terrible. In Europe there are several budget airlines that will get you to Greece or Spain or wherever for a very reasonable price. It won't be pretty but its a short flight and you'll have some money leftover for your trip. In the land of the brave & free, all the airlines are rubbish. They're all like Easy Jet or that kind of low standard but charge insane amounts of money for very poor service. A flight to New York from LA will be at least as much, if not more, than a flight from LA to London. That's just silly.
If you must fly with a domestic airline I would recommend Jet Blue. Again, it won't be cheap but the staff are always funny and helpful and they have a website and app that actually work quite well, which is in itself is a rarity.
I flew in to Burbank last night from New York and as we landed the flight attendant announced that there is no smoking at Burbank airport "or indeed anywhere in southern California" which raised a few eyebrows from the New Yorkers on board and got a few laughs from the rest of us.
The Norton Simon Museum
We we're staying with friends in Pasadena and found this place just down the street. Great art galleries, easy to wander around, good air conditioning, it was very hot outside, and a plethora of wonderful paintings and sculpture, a great way to spend a few hours, far from the madding crowd, and they sell beer.
I fly back and forth between London and Los Angeles fairly regularly so naturally I've flown with pretty much all of them. My favourite used to be New Zealand Air and kind of still is but Norwegian do such a great job and they usually come in around two thirds of the price of their main competitors. This is because they don't fly to Heathrow as the fees there are astronomical, things like food, luggage and seat choice are extras so you can save at least $50-$150 there and the planes are all Dreamliners, much more fuel efficient than the clunky old 747's and they have much better lighting, climate control etc.
The staff on the ground and in the air are all very friendly and helpful and take at least some of the nightmare that is LAX out of the equation. They also have an app for your smart phone that, dare I say it, actually works! Bravo.