We flew to LA the day after the planes starting flying again post 9/11. In fact it was so soon afterwards they discussed at great lengths whether to let the child friendly scissors in my 3 yo daughter's art box on the plane - but then served dinner with metal knives. What the!
We never felt safer. Security was everywhere.
Disneyland was really quiet and Knotts Berry Farm (where we stayed) was so empty we stayed on the log ride around 10 times because there was no one waiting. The shuttle to Disney from the hotel was their stretch limo since we were the only passengers most days and it was cheaper for them to run than the bus. We were upgraded to a suite (because the hotel was empty) and upgraded to business class from LAX to Sydney - including a 3 year old.
The hardest part was enjoying ourselves when others went about their days in fear.