The terminal CO is in at LAX is a rather small non-distinct terminal with minimal services at best and probably none during the hours you will be there.
This makes it somewhat more appealing and secure to sleep in, if you ask me. There is also an open air terrace for smokers - so you can sit outside and get air (don't know if it's open overnight though).

If you decide otherwise there is a Holiday Inn on the corner of Century and the 405. Stay away from the Crowne Plaza!!!