Art Museums: LACMA (Los Angeles County Museum of Art) in west LA, Norton Simon museum in Pasadena, Getty museum (never been to the new location - always went to the original Roman villa in Malibu).
Disney Concert Hall in downtown Los Angeles - I keep meaning to get some photos of it. Also, zillions of little art houses if you know where to look in the downtown area. Griffith Park (Griffith Observatory, Los Angeles Zoo). Attend a movie at the El Capitan theater in Hollywood (now Disney owned - a beautiful theater that still maintains a stage). It’s right across from the historic Grauman’s Chinese theater (and yes, the whole area is kinda grubby and cheesy, but the interior of the El Capitan is gorgeous). The Hollywood Bowl is a pleasant place for an outdoor concert on a summer’s evening, though acoustically it sucks (and sometimes the coyotes give counterpoint). The Greek Theater in Griffith Park is the better venue for outdoor concerts (though now that I think of it, didn’t they just renovate the Hollywood Bowl)?
Santa Monica beach, though I prefer the south facing beaches for actually being in the water (Huntington, Bolsa Chica - forget those west facing beaches like Manhattan and Hermosa beaches). Never saw a riptide there in my life - and the mean and nasty Wedge in Newport for the high art of body surfing (up to 20 foot waves on a wild day breaking in one foot of water - surf boards not allowed).
The Hat in Pasadena for Pastrami - but it is on Lake just north of the 210 Freeway, not in Old Town Pasadena, a shopping/eating district that is kind of fun to walk up and down on a summer evening. Never understood the attraction of In & Out - Fatburger has a much better burger. Another distinctive L.A. burger is Tommies old-fashioned chili-burger, though likewise, I’ve never understood the attraction of the greasy thing, and the number of copies is frightening and confusing (Timmies, Timmy’s, Tommy’s, Tammies, etc. etc. on and on, every one trying to cash in on the cache of Tommies).
One other important thing: Los Angeles is a sprawl. It is rather a large geographic area with lots of miles between all the various locations every one has been mentioning. It’s not nice and compact like Manhattan, for instance.