The problem with having less than a day in L.A. is that there is so much sightseeing of all sorts to choose from. It's not concentrated in one area, and driving around eats up time (especially if it's raining).

If it were me, I'd just go to one place/area and hang out there for the day. I dislike Santa Monica and Hollywood, but lots of tourists don't. I think downtown L.A. has lots to offer in a small geographic area that's easy to navigate. I also like Pasadena, and the Norton Simon Museum and Huntington Gardens/Library there are both open on Monday afternoons.

http://tinyurl.com/ksmotzl

This was another discussion that's similar. I shared a link for how we spent our time before our flight to NZ