The attractions nearest to Union Station are Olvera Street, the Chinese American Museum, City Hall and Little Tokyo. Olvera Street is across the street from Union Station and the others are within 5-10 minute walking distance. Anything else will require a bus or train ride.
From LAX, a bus ride takes 30-60 minutes each way (including transfers). Take the FlyAway Union Station service from the terminal at LAX (look for a green sign on the lower level) to Union Station in downtown Los Angeles.
Click here to visit the Metro website for bus schedules
On the Metro website's home page, use the Metro Trip Planner:
To: Union Station
MTA's Metro Trip Planner displays schedules and fare information for LA metro buses and trains. It's fast and easy to use. Simply visit the MTA's website at Metro.net and you'll find the Metro Trip Planner on the top right side of the home page.
You will need a few hours to walk around and view the sites. So you will realistically need at least a 5 hour layover for this type of excursion. On planning for your return trip to LAX, don't forget to allow an additional hour to get through security and walking through the terminal at LAX.