The Flight Path Learning Center is a museum located at 6661 Imperial Highway and was formerly known as the "West Imperial Terminal." This building used to house some charter flights (Condor Airlines) and regular scheduled flights by MGM Grand Air. It sat empty for 10 years until it was re-opened as a learning center for LAX.
The center contains information on the history of aviation, several pictures of the airport, as well as aircraft scale models, flight attendant uniforms, and general airline memorabilia such as playing cards, china, magazines, signs, even a TWA gate information sign.
The museum claims to be "the only aviation museum and research center situated at a major airport and the only facility with a primary emphasis on contributions of civil aviation to the history and development of Southern California". However, there are other museums at major airports including the Udvar-Hazy Center of the National Air and Space Museum adjacent to Washington Dulles Airport, the Royal Thai Air Force Museum at Don Muang Airport, the Suomen ilmailumuseo (Finnish Aviation Museum) at Helsinki-Vantaa Airport, the Frontier of Flight Museum at Dallas Love Field, and others.
Here's the map with directions: http://www.flightpath.us/visiting.htm
6661 West Imperial Highway
Mailing Address: P.O. Box 90234, Los Angeles, CA 90009; (424) 646-7284.