Unless you are some sort of art connoisseur, scholar or frequent gallery-goer, you are doing way too many art museums. The museum with the best collection in the southland is actually the Norton Simon in Pasadena, but the best true museum-going experience (which includes factors like the architecture, site, vibe and things like food and amenities) is either of the two Getty's. I would pick one and call it a day for art museums. LACMA is in construction right now and will be for the next two years. Neither the Broad nor the Academy Museum should take you more than two and a half hours at most. So a mild diversion if you are looking for one.
I always give this advice for tourists who are here for the the summer, but the absolute best thing to do that is very LA is to take in a performance at the Hollywood Bowl. The site and atmosphere is super romantic. Do what the locals do and bring your own picnic dinner. Look online for some common places where Angelenos like to buy packaged picnic meals, or get creative and create your own. Pack some blankets for when the temperature drops over this hills and go take in a performance under the stars. It almost doesn't matter what is playing. Classical music or jazz is the most common, but they also do great things like musicals, musical sing-alongs, movie showings set to a live orchestra and plenty of pop music across all ranges. Don't worry too much, just go to what's playing on the day you're available. Unless it is some very popular artists, the Bowl rarely sells out and the upper seats (which are the best place to take in the views) are purposely kept fairly inexpensive. Highly recommend.
Also available during the summer that is unique to So Cal and found almost nowhere else: Laguna Beach's Pageant of the Masters. There's enough info online so I don't have to describe it here, but suffice to say it's an old art form that has basically died out and I can't name anywhere else on the planet that does something like it.