LA is huge and traffic can be very bad, so you need to plan accordingly. A five mile drive on the 405 could take 5 min when there isn't traffic (like 3 AM) or an hour or more at rush hour on a bad day. In LA, you need a car, public transport is minimal, also the area around LAX is not particularly interesting and there is nowhere to walk to.
For one day, I'd drive up the coast, starting in Santa Monica, and head up to Malibu canyon or further if you're enjoying it There are great views and nice restaurants long the way. Depending on your budget and time, you could stop at Jeffrey's in Malibu (right on the water but expensive) or the Reel Inn (near Topanga and inexpensive) or a number of others. The drive would be about an hour if you take it slowly.
From there, I'd take Malibu canyon to the 101, about 20 min, but you could stop to hike in Malibu canyon if you enjoy the outdoors. Then take the 101 East across the San Fernando Valley to Hollywood (45 min without traffic) and walk around. Perhaps see the Chinese Theater and other land marks there. For a longer day, continue East to Pasadena where there are great museums and a nice downtown.
From there, you could cut across Westwood, back towards Santa Monica. Santa Monica is fun to walk around and the you'll be relatively near the airport. This is best done on a weekday, avoiding the 101 across LA between 7 and 9 AM and 3-6 PM. It would also work on a weekend.
I'm not sure I'd go to Disney Land, since I've heard Disney World is much better, but I'm not a huge fan either way.