I think the Southbay definitely has a stranglehold on the most izakaya spots in LA, probably owing to the high number of Japanese transplants (not Nisei or Sansei). Thought I would start a thread to ennumerate the different restaurants and rank 'em.
I personally really love Musha by Mitsuwa market in Gardena. Their pork belly and flamed mackerel are awesome!
I've recently been to Izakaya Yuzen Kan in Torrance on the corner of Crenshaw and PCH about three times now. The first time I went, I loved it, but the last two were disappointing. The waitress forgot my dad's order completely and the tempura was waaaay too oily.