If you are going to The Huntington (Gardens), I suggest making a reservation for tea at the Rose Garden Tea Room.
http://www.huntington.org/tearoom/
Just looking at the menu is making my mouth water.
I also second the suggestions for adding the Griffith Observatory to you itinerary. Admission and parking are free, which is rarity in Los Angeles. An evening visit provides for an amazing view of the city lights.
Just to clarify @OHMomof2 the Expo line is run by Metro which is LA bus/light rail provider. I’m one of the lucky few who can take Metro trains to work every day. Here’s their website: https://www.metro.net/
Metrolink are commuter trains, real trains, that run out of Union Station. They can be useful to get to places not in LA proper, like Burbank, Anaheim, Pomona, but their schedules are designed for commuters and they don’t run as often as the light rail. Some lines do run on weekends though.
There is no Metro service directly to LAX. There’s a light rail there, but I never take it. I either take Uber, or the Flyaway Bus. The Flyaway Bus goes to Union Station, and from there you can take the subway/light rail.
@4mummy, unfortunately, LAX lags way behind other cities in public transport. You might look into booking a hotel near the airport that offers free shuttle service to and from the airport. The Embassy Suites in El Segundo is nice, but there are many options and it’s worth searching for special deals. From LAX you can take the Flyaway bus for $10 to either Union Station or Hollywood (http://www.lawa.org/flyaway/). The laws were recently changed to allow Uber to operate at LAX, so that’s another option if you’re not renting a car. As OHMomof2 mentioned, Uber share (carpool) is very affordable and you meet some interesting people! The closest nice beach town is just 15 minutes (non-freeway) south of LAX, Manhattan Beach. It’s become very upscale over the years so I suspect lodging prices will be high, but might be worth a look.
If you want to see the sights but let someone else do the driving I highly recommend the “Day in LA” tour company
(http://www.adayinlatours.com/). They start in Santa Monica and visit Venice Beach and points north. They do not visit downtown LA, which is best explored on foot anyway. The guides are good, buses are comfortable and the emphasis is on LA culture and history, not focused on movie star homes. Here is the list of hotels for which the tour company will provide free pick up (many airport hotels listed): http://www.adayinlatours.com/hotel-pickups.html.
Thanks for clarifying @trojanchick99 - I saw the train line out to Santa Monica and the station in Hollywood, found wrong web site.
A family member works in urban planning in LA and was very excited about the “beach train”.
I take the Expo Line every day and am so happy it now goes all the way to Santa Monica. I used to live there, but once I moved East, I would hardly ever go because traffic is so nightmarish. The ridership on the Expo has jumped considerably since they opened the extension.
Thank you so much everyone for your suggestions. I will have fun following them up.
I agree that the Huntington Library is one of the few “must-sees” in the LA area but I dissent from the suggestion to have tea there. If you are interested in afternoon tea, the Langham Hotel just down the street has a much better one in a room with a spectacular view. Or, go for Shanghai soup dumplings at Din Tai Fung in Arcadia (20 mins away) as someone suggested upthread. There’s usually a wait but it goes very fast.
For restaurants, look up Jonathan Gold’s LA Times annual supplement of the top 101 restaurants in LA, which covers everything from fine dining thru modest ethnic restaurants.
Sorry for the hijack, but what’s a good place for Dim Sum over on the West side near UCLA? We’re dropping D off there next week and will be staying over the weekend.
Did anyone mention the Holocaust museum, or the museum of arts and crafts?
^Do you mean the Craft and Folk Art Museum (www.cafam.org)? One could spend more than a day in the Mid-Wilshire/Hollywood area between CAFAM, LACMA, LaBrea Tar Pits, LA Farmers Market, Holocaust Museum, CBS Studios, The Grove (if mall store shopping’s your thing), Melrose Ave., Hollywood Bl., etc., etc., etc.
I definitely like the Gettys idea. The Sepulveda pass site is beautiful architecturally with amazing views of the LA basin. The Malibu site feels so luxurious with amazing ocean views. You can make reservations for tea there, too, though it’s expensive for what it is, but you can’t beat the views or the weather.
The Huntington in San Marino is also a great idea, and you could easily throw in a tour of Caltech 
(we are on CC, aren’t we?). We just spent our anniversary strolling Colorado Bl. in Old Town Pasadena while our son was at a birthday party nearby. I’d have to say, it’s not what it was. We found mostly restaurants, bars, and mall stores. But, it is a pleasant place to be.
If you are going to Pasadena stroll through the Caltech campus - one of the prettiest campuses ever. (Though it would have been prettier if Bertram Goodhue’s blue domed central building had been constructed instead of the 1960s tower that is Millikan library.) I also agree Huntington Gardens is worth a visit.
I lived in L.A. years ago, and we were lucky to be able to spend a few days there this summer. Here’s my list:
I recommend the Hotel Angeleno, www.hotelangeleno.com. It didn’t cost much more than the nearby Holiday Inn Express, and it was a lot nicer. The restaurant is pricey, so it is probably cost effective to use Uber to get to Westwood for major meals.
Stop at the Santa Monica Pier and/or Third Street Promenade after you leave LAX airport. We had lunch at a sit-down restaurant on the pier.
Getty Museum, for sure! The Hotel Angeleno has a free shuttle, or you can take Uber. I was so taken with the views of L.A. and the gardens that we ran out of time and didn’t get to see much inside. You can have lunch on the patio.
If you are into Disney, the drive from West L.A. to Anaheim is not bad on a Saturday if you leave L.A. early and come back late.
Universal CityWalk at the entrance to Universal Studios has plenty of shops and restaurants. The view of the San Fernando Valley from the parking garage was fantastic!
Uber is very fast on the west side of L.A. Wait times were around 5 minutes.
Enjoy your trip!
If you do Universal City Walk and are feeling adventurous you could try iFly. It’s an indoor wind tunnel to simulate sky diving. https://www.iflyworld.com/hollywood/
And if we are adding amusement parks, Universal has the new Wizarding World of Harry Potter.
If you visit Orange County (Disneyland) That opens the door to even more possibilities.
Thanks to all for the suggestions. Didn’t have quite as much time to play tourist due to family needs, but did get to the Getty Center which was amazing. The architecture tour was very interesting, even more so than some of the art. Some interesting restaurants as well.
Also made it to the beach, on a very warm day.
However, not sure how you all deal with the ridiculous traffic at all hours. Maybe we were unlucky (other times not quite so bad outside of rush hour). I read that more transit options are coming.
The Museum of Jurassic Technology!
I just got back from a business trip to LA. It took me 90 mins to drive the 10 miles from the hotel to my meeting this morning. You know you’re in LA when you give yourself 2 hours to drive 10 miles. And then an hour into it you start worrying about being on time.
^^^ I should add that it’s not always that level of horrible. Frequently very bad at most hours for sure though.
The traffic has gotten insanely bad over the last few years. I’m not sure what happened, they expanded the 405 and it made the traffic twice as bad. It makes no sense.
A Murphy’s Law of some sort. The traffic will expand to fit the lanes available. All the housing built over the past 30 years. All the eccentricities of how business pockets are spread out in many LA communities. And more. I commuted through that mess for years.
Other areas do have just as bad a problem.