I would second Santa Barbara over Palm Springs. Closer, easier to get to and more to do on a short trip. In April the weather should be beautiful. Rent a surrey and cruise along the beach or check out the Santa Barbara Zoo. Its less daunting than the LA or San Diego zoos and has beautiful views.
http://www.santabarbarazoo.org/
If you want to stay closer to LA, why not stay in a hotel on the beach in Santa Monica? Depending on traffic you can reach Santa Monica in 20 minutes from LAX.
Anyway, thats my two cents. Enjoy your trip!
[This message has been edited by kef0913 (edited Nov 26, 2003).]