Southern California has several places to visit if you are interested in space, aviation, or astronomy. A good list of Aviation Museums can be found here. A good list of Observatories can be found here.
The Columbia Memorial Space Center in Downey, CA is dedicated to teach young people about careers in space exploration and aviation. They focus on engineering, technology, and science.
The California Science Center in Los Angeles is soon to be the new home of the Space Shuttle Endeavor. In addition to their many science related exhibits, they have a special Air and Space Gallery.
The San Diego Air and Space Museum in San Diego has an extensive collection of significant air and space history and technology – from older military aircraft through space exploration.
The Discovery Science Center in Santa Ana features exhibits from all facets of science – including aviation and aerospace.
The Griffith Park Observatory near Los Angeles has a spectacular planetarium and much more
March Field Museum at March Air Force Base is East and South of Riverside on the 215. They have a good collection of aircraft of all ages.
The Air Force Test Flight Center Museum at Edwards Air Force Base chronicles the test flight history at Edwards. The museum is open to the public (without official base access) only twice each month, and by reservation only (see web site for details).
The Castle Air Museum in Central California near Atwater has another good collection of aircraft
The Aerospace Museum of California at McClellan Air Force Base near Sacramento has an extensive collection of aircraft and some space vehicles.