Flyaway Bus Service Between Union Station and LAX
Head out of LAX and into Union Station using the Flyaway (make sure the head sign says "Union Station" as there is also a Flyaway Bus Service to Van Nuys). For only $3 one-way, you can find your way to Downtown LA and at Union Station, a major LA transportation hub.
Passengers departing LAX are picked up on the Lower/Arrivals Level in front of each terminal under green signs marked "FlyAway, Buses and Long-Distance Vans."
Buses run in both directions every 30 minutes between the hours of 5 a.m. and 1 a.m., and every hour from 1 a.m. to 5 a.m. The buses depart Union Station and LAX on the hour and half-hour. The 20-mile (32 kilometers) ride takes less than 45 minutes during peak traffic periods.
More Info on the Flyaway>>
Once at Union Station, you have a number of opportunities by foot and rail to experience LA. Take your pick!
By Foot - If you don't want to roam too far, right across the street from Union Station's main entrance you can explore El Pueblo de Los Angeles, the birthplace of Los Angeles featuring historic architecture, museums, and shopping at Olvera Street. A little further on foot, you can walk to Chinatown for a variety of Asian foods, shopping, and culture (Chinatown is also directly accessible by using the Metro Gold Line.)
By Rail - Go Metro on the Metro Red Line! Only $3 dollars all-day pass or $1.25 one-way, it's an inexpensive and easy way to get around.
Civic Center Stop features the arts and culture of Grand Avenue's museums, architecture, and restaurants. If you don't mind a bit of a stroll from the station (roughly a half mile), you can walk into the Little Tokyo area, or you can catch the DASH A (Weekdays) or DASH DD (Weekends) to head into that direction.
Pershing Square Stop is home to Los Angeles' Historic Core. For early morning travelers, the Grand Central Market has many great treats to find. Check out the historic theatres and buildings of the area. If you're looking to purchase jewelry, this area is home to the Jewelry District.
7th/Metro Stop offers shopping and eats at 7th/Fig and nearby Macy's Plaza. The South Park area is home to the Fashion Institute of Design and Merchandising which generally has a museum exhibition, the Museum of Neon Art, and Grand Hope Park.
Wilshire/Western, Wilshire/Normandie, and Wilshire/Vermont Stops take you into Los Angeles' Koreatown. Explore great Korean food, karaoke, and culture.
Hollywood/Western Stop takes you into the heart of Thai Town. Enjoy great Thai food and shopping!
Hollywood/Vine Stop takes you to historic Hollywood theatres including the Pantages and the Avalon. Roam down Hollywood Boulevard for ecelectic shopping, arts, and the Hollywood Walk of Fame.
Hollywood/Highland Stop is an entertainment destination. From shopping at the Hollywood/Highland complex to eclectic museums and historic sites such as the Graumann's Chinese Theatre, there's plenty to do in this area of Hollywood.
Plan your time in these locations accordingly to get back on a Flyaway bus and get to LAX in time!
At the Green Line, make sure to buy your all-day Metro Pass for only $3 (valid throughout the day of your purchase) and head out on the Green Line toward the Metro Blue Line (Green Line Heading: Norwalk). Transfer to the Blue Line at "Imperial/Wilmington - Rosa Parks Station". 
At the Blue Line, make sure you're heading southbound to Long Beach. In approximately, a half hour from your transfer, you'll be in beautiful Long Beach. Major stops for the Long Beach area are Fifth Street Station, First Street Station, and Transit Mall Station. 