Best breweries near LA?

Depends if you are willing to venture very far from Hollywood area. Most of the popular breweries are a bit of a drive in either direction though there are some newer breweries opening closer to downtown LA. The Surly Goat has a pretty solid tap list though not so focused on local brews when I last visited.

Moderately close to you are a few Karl Strauss locations as well as Highland Park Brewing, Three Weavers, and El Segundo Brewing but the issue is traffic it takes to get out to either of them might be a bit much. It all depends on whether you are renting a car and don't mind getting stuck in traffic. I haven't been that impressed by Angel City Brewing but there is the newer Arts District brewing in downtown LA that looks interesting at least from the tap list. Others can comment on the beer I hope.

 

I loved MacLeod up in the valley. Monkish and El Segundo are can't miss stops. And the Vendome on Robertson has a great bottle selection, check out their instagram.

 

Went to Monkish, Smog City and Phantom Carriage last week. I'd go back to all of them. They're all South Bay which is quite a drive, be aware of that.

 

Melrose wine and spirits can get some good stuff. It's like a bodega so not a huge selection. That's the only good shop I know in Hollywood. blue Palms has a consistently great tap list and it's right in the heart of Hollywood.
If you are going to drive one day then I would recommend hitting up El Segundo, Monkish and Smog City. They are right next to each other. Phantom Carriage is close too but every time I go they are out of their good sours.

 

Never been bottled

 

In/around City of LA (not counting South Bay) to me the top tier of breweries are Highland Park Brewery, Three Weavers, and Mumford. Next tier MacLeod's, Arts District, and Craftsman (no tasting room but available at Lucky Baldwin's in Pasadena). Brewyard in Glendale also has some interesting "ale'd" lagers.

Best bottle shop near Hollywood is Sunset Beer Company on Sunset Blvd in Echo Park