Leaving aside the fact (opinion?) that LA rainy weather is relatively mild and shouldn't keep you inside of you're dressed appropriately or at least have a decent umbrella:

Generally:

https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=indoor+los+angeles+activities


http://www.discoverlosangeles.com/insideLA


From my admittedly limited personal experience:


Getty Museums (there are two - the main one off the 405, and the "Villa" off of PCH kinda between Pacific Palisades and Malibu)

Peterson Automotive Museum https://petersen.org/

Long Beach Aquarium http://www.aquariumofpacific.org/

California Science Center (adjacent to USC) has one of the now-retired Space Shuttles (the Endeavor, I believe) https://californiasciencecenter.org/

There are plenty.

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War is god

Go to Whole Foods in Brentwood and check out all the camel toe.

You'll thank me later.

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Civilize the mind, but make savage the body.

- Chinese proverb

Watch everyone freak out because it's raining?

You beat me to it. Forget that Whole Foods for food because it is a small store. Hit up the Bristol Farms on Wilshire in Santa Monica for a decent prepared meal.
The rains will be no big deal and much less than those from two weeks ago that flooded freeways. If you are interested In driving at K-1, jump around at Skyzone before or after as they are very close in Torrance. If you want to go for a swim, do so at the mouth of a storm drain in Long Beach near the aquarium.

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DISH is how we do it.

Yeah. We said fuck it and are being grown ups and walking around. Screw the rain

It's gonna rain like .5" at most today and Sat / Sun will be clear.

Shoulda been here last couple weeks for some actual rain