No one mentioned the Autry Museum yet? Adjacent to Griffith Park, near Burbank. Also consider the Petersen Auto Museum if you like cars. It's on Wilshire Blvd in West LA. Check out Philippe's near downtown/Chinatown for some original french dip sandwiches (try the lamb).
Also be aware that the traffic never lets up, it is a 24/7 phenomenon now. Allow plenty of driving time, one crash in the wrong spot and the whole LA basin comes to a stop.