Well Steve, it depends on how late you will be there.
LAX has ops 24 hours a day, though between 0000 and 0600 or so, they operate completely over ocean, so In N Out and The Proud Bird are out of the question. Dockweiler State Beach closes at night and the lifeguards are pretty strict about kicking people off. In N Out is open until about midnight-1AM, so you can watch ops there and eat their famous burgers till the midnight switch over. As for internet, there are public internet kiosks in TBIT that are accessable pre-security, and they afford a nice view of some of the gates where you will see tons of 747 action in the evening. Additionally, there is plenty of food there.