Reminiscent of the field museum in Chicago, Los Angeles County has its Natural History Museum complete with a taxidermy dioramas from around the world and prehistoric fossils through the ages.
This museum is free on Tuesdays from September through June. Even during the summer months, a stroll through the dimly lit jam room is an educational break from the summer heat. Plus you get to look at shiny things!
Check out the calendar at EmilieBroughton.com for more happenings around LA. I also try to include free days (and mostly free days) for various museums and cultural happenings. If you know of any, feel free to drop me a line so I can add to the calendar.