What to do with an 8 hour layover at LAX
 

We will be flying to Vancouver via LA with an 8 hour layover at LAX. Any suggestions for a short ( 3 - 4 hour ) tour in LA. We would prefer being picked up and dropped at the airport so I assume this would need to be a private tour service, or whether to just get in a cab and say show me the sights for 3 hours.
Duddite

Where are you coming from that you could not fly directly to either Vancouver or Seattle?
What do you plan on doing with your luggage after you clear Customs and Immigration?

I've been in this situation a few times; usually we rent a car and go to Manhattan Beach area, shopping and/or for a meal. It's a really lovely area. I'm not at ease with travelling too far, since the traffic back to the airport can be horrific. Might venture as far as Santa Monica but have been stuck in traffic, very unpleasant.

Consider renting a car and going to one of the beach communities near LAX...Manhatten Beach, Hermso Beach, Redondo Beach. Or as Odin adds, maybe Santa Monica. Just be aware that LA traffic between Santa Monica and LAX can be a nightmare at any time of day.

thank you all for your advice.
I am flying from Melbourne Australia which has no direct flight to Vancouver.
I hadn't thought of renting a car, that might be the go.
I will have a look on Google Earth and see how far Manhattan Beach is.

It's not far, used to live there and work from the airport, just avoid rush hour traffic. Be sure and visit the pier and watch the surfers and beach volleyball players, lots of nice restaurants to have a bite to eat. There is also a nice small mall at the north end of Sepulveda Blvd. with two Macy's stores, if you show your passport you can get an 11% discount.

If you have the time, you could ride the Coast Starlight Amtrak train all the way to Seattle Washington. Amtrak runs two buses and 2 trains daily from Seattle to Vancouver.If you did not want to ride the train that far, you could also go to San Francisco and fly to Vancouver from there.

I'd take a walk along Abbot Kinney in Venice and have lunch at Gjelina.

I agree Manhattan Beach is a great option. Great place to spend a few hours. Awesome beach, great shops and restaurants, beach volleyball. Classic so cal. Close by is also Venice a bit north or maybe Hollywood park (racetrack) check to see if their are any events