If you're not fussy about exactly where you stay, you could book a hotel with priceline.com.

I'll be at the LAX Sheraton shortly @ $40 (plus $5 promotion) - accepted first time so I may have overpaid.

Stayed last fall at the LAX Marriott and LAX Renaissance - again accepted first time, so perhaps I overpaid.

Points on extras but probably not on room rate.

The LAX option on the priceline page is more likely to offer low rates than others. We're paying as much as $60 + $5 promotion for the Four Points Santa Monica.