Agreed about SF and LA - I found San Francisco much more interesting.
But as you are based in LA:
I thoroughly enjoyed a trip to Famous Dave's Barbecue - it is a chain, but the food was good and plentiful, and if there is enough of you, you can go for their Famous Feast: "A full slab of St. Louis-Style Spareribs, a whole Country-Roasted Chicken, 1/2 lb. of either Texas Beef Brisket or Georgia Chopped Pork, Creamy Coleslaw, Famous Fries, Wilbur Beans, four corn-on-the-cob and four corn bread muffins." All served out of a (clean) trash can lid.
They have a couple of places around LA - see map at
http://www.famousdaves.com/One thing I thorougly enjoyed at LA was the trip around Warner Brothers. Forget Universal Studios - it is a glorified theme park. Warner Brothers is a working studio, and the last to have an extensive backlot in LA (backlot = external sets). I did the very expensive deluxe tour, which gets you into the technical areas, but I understand the standard tour is also good. You do need to book in advance to be certain, though.
http://vipstudiotour.warnerbros.com/A less expensive trip (i.e. free). On a drive down to L.A., my hosts asked if I wanted to visit "Planet Vulcan". Being an old Star Trek fan, I said "sure". We ended up at
Vasquez Rocks, which is a 900 acre park, only 40 miles outside LA. It has very striking and varied rock formations all around - if you look one way, it looks like something out of a Western, look in the other direction, you are on an alien planet. Which means it has been used a lot for all sorts of TV shows and Films, such as Blazing Saddles, Army of Darkness, Bonanza, Mission Impossible, and - of course - Star Trek.
As others have mentioned, La Brea Tar Pits are worth a look, and I also enjoyed a trip to the
Griffith Observatory, which has a great museum and planetarium. Having said that, I went there because it is *the* observatory in James Dean's "Rebel Without a Cause". Yes, I'm a bit of a film nut!