I've been to LA a couple of times as part of USA hols.....
I wasn't impressed with LA per se, unless youre interested in the parks.....Universal, Disney and somebodies farm
And everything is so spread out you have to drive which means no drinking....and smoking for that matter....
There are the obvious tourist areas:
La Brea Tar Pits (interesting)
Chinese Mann Theatre and Hollywood walk of fame (crap)
I did enjoy a drive around the hills...mulholland drive...great views....and Bel Air and Beverly Hills
The Griffith Park Observatory was being refurbed when I was there but is probably open now. And you get to see the sign close up
And I don't have to tell you about driving in LA....it can make the M25 seem empty
BUT
That was until I found Santa Monica....great place....really laid back, beautiful beaches, great bars, nice (beautiful people). Who will chat to anyone.....i.e. they chatted to me....they love the british
The pier is nice, and there is a good shopping area.
It can be a little TOO bohemian and liberal if your a Daily Mail reader, and all the women dragging their chihauhau rats about as they go to yoga is a little irritating. And everything is all organic, carb free and fair trade.
But just go and get yerself a beer and people watch on the beach boardwalk.
Venice beach is just a cycle ride away, but is a no go area after dark and can be a bit full on at weekend....it can resemble Blackpool Prom full of tat at times.
Other things I have done within driving distance......Death Valley....absolutely beautiful....and obviously Las vegas and the Grand Canyon., Red Rock and Valley of fire
You may even consider an internal flight to Las Vegas....but it is deffo driveable....about 5 or 6 hours.
There are supposed to be tours of the Film and TV studios (not just Universal) at Burbank. Including being in the audience for some recordings...but I never went
I also went Palm springs, a couple of hours away and the Joshua Tree NP. Palm springs is desert and not really much there apart from old people and when I was there it got to 108 faranheit. But it has a cable car that goes up about 3000 feet and you watch as the temperature drops 25 degrees cent and go from toasting to there still being snow on the ground
Hope this helps
Bumper