I would suggest a trip to The Original Farmers Market on 3rd and Fairfax (not far from where he lives). Lots of nice places to eat while you are there as well - and try the Princess cake at the bakery (green, but it is really good!).
And directly next door is CBS, so in case you wanted to order free tickets to go to Price Is Right, or see any of the shows there, you only need write in advance to get them.
Up the street (North) on Fairfax is Canters Deli, a great place to eat!
And up Fairfax a bit more is Melrose Avenue - some nice shopping and worth a slow walk to see the shops (although it isn’t as fun and edgy as it used to be).
And further up Fairfax, turn left on Santa Monica Blvd and go about two blocks is French Market Place - a West Hollywood icon with food (again) and some interesting shops.
BTW, back to square one - if you go SOUTH on Fairfax from The Farmers Market, and go to Wilshire, you are at the LA County Museum of Art, the La Brea Tar Pits and the Petersen Automotive Museum.
All of this is not far from where your brother lives - and if he hasn’t seen them all yet, he should!
Have an In-N-Out burger at the location near LAX. Sit outside and eat and you will see huge planes coming in or taking off RIGHT over your head. It’s loud, but a very cool experience.
Visit the Santa Monica pier. It has all the charm of a 1940s pier–complete with rides (ferris wheel etc) and the good old pier food that clogs your arteries.
Take a gondola ride around Naples. Beautiful and relaxing, plus they let you bring your own wine and food.
And you really have to take a walk down the Walk of Stars. So historic and cool.
If you like record stores, Amoeba on Sunset is a very cool store, in addition to being very large they have a stage and bands will pop in and play free concerts… I’ve heard. I’ve been to the store many times but never when a band happened to pop in.
I’m sure I’ll think of more stuff as I lived in L.A. for a good stretch of time.
You could pop over to my old friend Jose’s house and tell him hello for me if you would be so kind ha ha. Alas a poor attempt at humor.
As I said I’m sure I’ll spew more ideas as my poor brain recalls them.
I also second the idea of the zoo, I love the L.A. zoo, and the Getty museum idea is splendid if you have any interest in art. The bike/pedestrian path at Venice beach is a lot of fun as well to stroll along.