The Los Angeles International Airport has the least expensive hotels in the area and the free shuttle from the airport can take you straight to your hotel (please call ahead of time to figure out the schedule). The airport is a 45 - 60 minute drive to the Jan & Frank Day House in Malibu.
The following hotels are right next to the airport:
Sheraton Gateway Hotel ($149 - $200)
La Quinta Inn & Suites by Wyndham ($113 - $160)