Spirits local to Los Angeles
Greenbar Collective is the only LA distillery which I'm aware of to open post prohibition. They are generally well thought of but I can't personally vouch for them.
Here's their website where you can peruse their lineup:
There might be SF based distillers whose products we get that you might not be able to find on the east coast. St. George's and Lost Spirits come to mind.
Your best bet to get something unique though might be in bitters, which would also be easy to pack. I'm a big fan of Miracle Miles Bitters, especially their Chocolate Chili Bitters. Bar Keep in the Silverlake neighborhood has a great selection and keeps open bottles for sampling.
You might also want to stop by K&L Wines if you are in Hollywood. They have a great selection, good pricing, knowledgable staff and they also buy single casks from distillers which they have bottled and are exclusive to them.
While its not LA based, I'd imagine that we have a much greater selection of tequila and agave based spirits than you would have access to on the east coast. Ramirez Liquors in Boyle Heights probably has the best tequila selection.
Hope that helps.