The La Brea tar pits are a good way to kill an hour or two. There’s a small museum associated with the tar pit.
Get the #19. Pastrami on rye with Russian dressing and coleslaw.
The Hat is good, but I don’t fine their pastrami to be anything special. However, the portions are gigantic. 3 people can eat their chili cheese fries and be full
On a nice day I don’t think there’s a better along-the-coast drive than just heading up PCH to Point Mugu. Lots of interesting scenery and plenty of spots to turn off and soak in the SoCal sea-and-sand experience from Santa Monica to Malibu and points north. If you go just a bit further, there’s a pretty neat Air Museum at the Camarillo Airport.
If you’re into antique cars at all, the (free!) Nethercutt Museum/Collection is definitely worth a 25 mile drive up to Sylmar (the Collection tour is by reservation only, but it’s free and a must-see).
Not mentioned yet and also worth checking out: the off-the-wall and strangely fascinating Museum of Jurassic Technology.
Thanks for that.  I did try to search, not sure how I missed it. Tons of great info in both of these threads.  Keep it coming! 
Traffic (and ways of avoiding it) is something that fascinates me. From watching SNL I am led to believe this is an Angeleno pastime as well. I do have one specific traffic question. If you were going to drive from Redlands to Westwood on a Friday afternoon, say rush-hour-ish, what do you think would be the best bet? Looking at the map, I’m thinking of a few options:
[ol]
[li]The 10 all the way to the 405 north.  I’m guessing this is a nightmare since it goes right through downtown?[/li][li]The 10 to the 5 to the Ventura Freeway and then the 405 south.  Looks like quite a bit more distance, but would traffic be any better?[/li][li]The 10 to the 101, then surface streets (Santa Monica/Wilshire? Hollywood/Sunset?)[/li][li]Some other option?[/li][li]Just don’t.  Wait until 7 PM or so.[/li][/ol]
If I do end up needing directions, or just discussing the best way to get somewhere, what are the colloquial names for all these freeways/highways?  Do locals generally just call them “the 10”, “the 5”, etc?  Or do they use names?  I hope it’s the former; I find numbers much easier to remember than names.
Along the same lines: are there any local customs/“dos and don’ts” I should know about? Similar to not calling San Francisco “Frisco”, or ordering a Budweiser in Portland. I have kind of a thing about sticking out as an obvious tourist.
Thanks again!
Woof, that’s a pretty long drive. I would say the 10W probably won’t be too bad until you pass the 5 (and you can just refer to the freeways by their number). All bets are off if there’s an accident somewhere. With usual rush hour traffic, I would say 2 to 2.5 hours for that trip. I wouldn’t bother switching freeways unless your GPS indicates that traffic is entirely clogged for the 10W. The switches will take more time than they’re worth and during rush hour, the 5 and the 101 are equally jammed. You can wait until after 7pm for traffic to clear up, but why would you spend more time than necessary in San Bernardino County? 
You can always drive halfway to Monterey Park or Alhambra and get some great Chinese food if you find traffic insufferable. I don’t know if you had bubble/boba tea before or if it would interest you, but there’s a popular local chain called Half&Half that serves milk tea. A little further north in Arcadia, there’s a Din Tai Fung where you can get xiao long bao, those little steamed dumplings. It’s part of a Taiwanese chain and you can see their chefs make the dumplings behind glass windows.
If you’re on the westside anyway the Getty is a no-brainer. As people said, it’s just a great place to hang out even if you aren’t into art. Downtown is hit or miss. I would check to see if there’s stuff going on in/around UCLA at that time.
Make sure you bring a GPS with you (if your phone doesn’t have it). The only map I ever recommend is the AAA LA Freeway map, it’s awesome.
Redlands to the Westside is a soul-crushing trip. Wow. Traffic will be absolute murder during rush hour and after 7 will barely help. If there’s any possible way to do this mid-day or Saturday morning, I’d take it.
I disagree with stopping somewhere halfway, you’ll spend an hour just exiting and entering the freeway again in the San Gabriel area. And the carpool lane won’t help since it’s 3+ for at least part of it (I forget where it changes).
You could headaup the 215 to the 210 and then stop off in Pasadena. You could go to Old Pasadena, or Cal Tech, or Huntington Gardens as mentioned. The Norton Simon Museum is a world class art museum Jet Propulsion Lab does tours, I believe but call in advance.
It is possible to take that long, but I usually find traffic in the San Gabriel Valley to move at a decent pace. It probably wouldn’t be a good option if MrSquishy is concerned about getting to Westwood as quickly as possible, but it could be a good option if traffic is very heavy and they wanted to take a break from driving and get some food. There’s some great taco shops in East LA along the 10 as well and he could always take the 101 from the 10 and drop by Little Tokyo as well. Phillipe’s is around the Downtown area too and they serve an amazing french dip sandwich.
One note about Langer’s - unless they changed their hours, they close at 4pm each day. I’ve heard people say that the area can be a little sketchy, but it seemed fine to me during the day times.
As mentioned, you can’t really get too close to the Hollywood Sign, but if you want a better view than from the streets below, head to Runyon Canyon Park. The trails up the canyon are fairly steep, but it’s a short hike. At the top is a good view of the sign and almost the whole LA basin below. It’s a great place to take photos, particularly if your camera has a panoramic function. It’s also not uncommon to see celebrities jogging or walking their dogs there, if you’re interested in that sort of thing.
And I second going to In-N-Out.  Some of the best fast food burgers and fries out there.
And Carney’s, the diner on Sunset that is inside a train passenger car.  It might sound touristy, but at 2 AM everyone loves it.  They have great chili dogs.
Don’t rent a convertible Mustang.
Don’t take a picture of the Beverly Hills sign.
If you’re ordering at a Mexican restaurant, pollo (chicken) is pronounced poy-o.
Always expect a few extra cars make left turns at intersections after their light has turned red, particularly during traffic.
(Note there are two County museums–the Natural History Museum in Exposition Park, and the County Museum of Art (commonly known as LACMA) in Hancock Park.)
ETA: Wait, three County Museums if you include the Page next to the Tar Pits.
There are also two Getty museums–the Getty Villa which specializes in the Classical Mediterranean cultures, and the Getty Center next to the 405. The Villa is quite impressive in the way they have duplicated an entire Roman villa in pristine condition. The collection is not as good as it once was, since they had to return a good deal of their best objects to Italy and Greece, but it’s still well worth seeing.
The Getty Center covers visual art, mostly painting from the early Renaissance through the 20th Century. The collection isn’t as good or comprehensive as LACMA, nor the Norton Simon for 19th and 20th century works, but as Procrustus said it’s an amazing site. There’s also an expensive but excellent restaurant where the two of you might want to take dinner following an afternoon at the museum. Both museums are free to get in but you have to pay for parking, and reserve it in advance.
The NHM is supposed to be the largest natural history museum west of the Mississippi, and you’ll recognize the East Rotunda from quite a few films and TV episodes. The gem and mineral collection is stunning and one of the best in the country. The adjacent Rose Garden is well worth a look in season, but you’ll probably be a little to early for that.
Wow, I guess I do like museums.
Whatever you do, have fun, and remember to drop the “I-” and add the article when referring to the freeways. Otherwise you’ll only startle and confuse us. Older people still use original freeway names like the Santa Monica Freeway, but most people now just refer to them by their numbers. Nobody actually uses the revised names that have been bestowed in the last decade or two, like Rosa Parks Memorial or Christopher Columbus Transcontinental Highway for the 10.
Speaking of Mexican restaurants, if that’s your thing you should definitely go to the Golondrina on Olvera Street.  Food and margaritas to die for, but be careful with the latter.  You might want to take the train in for that one. 
Of all the Mexican food places I’ve eaten, Loteria Grill at the Farmer’s Market is my favorite (Loteria is a chain, FYI). But it’s a little nouveau, not traditional (lifelong Angeleno talking here). And it costs a little more. But damn, their soft tacos are crazy good.