Hollywood Park features horse race betting and a casino. Must be 21 to bet, but anyone can go into the racetrack facilities. Horse racing is seasonal. Sometimes there are live races at Hollywood Park, and other times the races are simulcast from other parks.
Getting there: From LAX, a bus ride takes 15-30 minutes each way (including transfers).
Time estimate: Hollywood Park is close to LAX so it won't take long to get there. So the amount of time needed depends mostly on how long you would like to stay. You will probably need at least a 4 hour layover. Don't forget to allow an additional hour to get through security and walking through the terminal at LAX.