I was thinking about your post last night radiogareth, and thought I'd mention a couple of other things
There's a pretty good aviation museum at the Palm Springs Airport. Check out http://www.air-museum.org/ if you have any interests -- their specialty is WWII aircraft, and they have quite a few, and a fair number of them in flying condition.
Depending upon your timing and other routes -- Edwards Air Force Base area/ Palmdale area in the desert north of LA (its about 2 hours north of downtown LA) is sort of a mecca for aircraft fans. There's a couple of musuems and open air displays up there that have a lot of cool aircraft, including the base musuem at Edwards. That's pretty much post WWII aircraft, but includes SR-71s and the like. If you're coming in from overseas, you'll need to write the base public affairs office before hand, or tag in on one of the public tours. There's a second site in Palmdale where they have SR-71 and U-2 displays at the factory they were built in.
Update June 2025 (RTA): The Edwards AFB Flight Test Museum is currently open only to those with base access, but a new museum is anticipated to open to the public in 2026.