Before you enter your terminal and pass security, go the Theme Building, kinda in the middle of the ring road that links the terminals. On the weekends, you can go the outside viewing deck on the top (we missed this, it closes at 5pm - when we arrived I thought we had a couple of mins up our sleeve, but were promptly told to turnaround and take the elevator back down - the deck was closed). So we headed to the Encounter restaurant and bar, a level below the deck, but you need to take a different elevator - confused! We had a drink at the Encounter bar, which is decorated on an attempt to emulate it's Jetson-ish Mid-Century Modern exterior. You may become mesmerised by the Lava Lamps. The best thing about this place though, is observing the planespotters that gather in the bar. I have no idea what they are doing, but I know they are very serious about it. They seem to spend their time peering through massive binoculars at landing planes and then making notes - I wonder if they are playing plane bingo?
So that's about it for how to waste time in LAX. If you need WiFi (and it is a need), you are going to pay $8 for the privilege (this $8 will last you for 24hrs of WiFi - here's hoping you would never need it for that long in an airport!). To access, just open your laptop, the T-Mobile page will pop up and you go ahead and pay by credit card: tip, you will be asked for a Zip code, and you will need to enter a US zip code, they won't recognize international ones.