Haru ULaLa (Downtown)
More grill focused. They also have an astounding assortment of gyoza, including shiso variants that are wonderfully piquant. $12 pichters of Kirin. Grilled rice balls. The egg custard wasn't that great... But this place is certainly heavy on the drinking end. Many nights I have seen a cluster of drunk folks smoking on the curb out front at midnight.
368 East 2nd Street Los Angeles, CA 90012-4203 - (213) 620-0977
Musha (Santa Monica)
A more modern forward looking izakaya with a hint of california influence, but astoundingly strong menu sure to impress traditional Japanese folks from Tokyo as much as your midwestern siblings. Aburisaba (marinaded mackerel that has it's skin blow-torched at your table), Oshinko (home-made pickles from various baby veggies), Okinomiyaki (a fluffy omelet with octopus). Plenty of great veggie options. This place always leaves you feeling upbeat and positive (and the latin jazz doesn't hurt the sunny vibe of their food at all). Can get busy, so make a reservation. Leans a bit more toward the restaurant end.
424 Wilshire Blvd Santa Monica, CA 90401 (310) 576-6330
Furaibo (West LA)
A very authentic place on Sawtelle where the masses eat before karaoke at the bar next door. They have some curious specialties such as tako wasabi (raw octopus with chopped fresh wasabi and a slimy texture). Dried lake fish with their roe still inside. The grilled chicken-part sampler is one of the gems. Solid veggie options. A rather traditional menu with a huge assortment of options. Try to sit on the floor in the traditional Japanese style room if your legs can handle it for a more intimate experience. Leans a hint toward the restaurant end, but I haven't been late at night. This place is always hopping with locals.
2068 Sawtelle Boulevard, Los Angeles - (310) 444-1432
Izayoi (Downtown/Little Tokyo)
Widely diverse menu. The flavors are distinctly more subtle. There wasn't an dish that really floored us, but most everything was solid. The best items tended to be things like the "Sardine Burger". Sure as hell avoid the miso squid leg and raw egg dish which made everyone gag. Sake is a touch pricey and the place was touch "hygienic" for my tastes. Far leaning toward restaurant (they even close at 10:30).
132 North Central Avenue Los Angeles, CA 90012-3913 - (213) 613-9554
Not a proper izakaya, but an amazing french/japanese restaurant in the izakaya-has-babies-with-a-wine-bar flavor. No reservations, but if you are sick of your usual wine bar flavors, the food here is killer and they have a large selection of moderately priced wine that focuses on sustainable and organic production. Solidly on the restaurant end and a bit pricey. The chef here is Shiro, famous for his Pasadena restaurant Cafe Jacoulet. Corkage is around $15.
Again, not an izakaya proper, since their specialty is on grilled skewers, but they have a good selection of other dishes from their neighboring restaurant Sushi Roku. Fois gras and lobster skewers as an idea of what they are known for. Pricey, trendy and small, this isn't a place I would personally frequent (especially with Bar Pinxto so close, and Musha in walking distance as well). Tends a bit toward the bar end.
Raku (On Olympic near Sawtelle)
Korean / Japanese traditional bar food. Plenty of different menu options. Tends to be a bit on the bland side. The sushi wasn't great, but something things like fried lotus root were tasty. The two times I've been there it was quite quite and not many people were around.
On my list to explore:
Sasaya (Santa Monica Blvd), Asahi (Downtown Los Angeles), Nanbankan (Sawtelle)
Let me know if you have more suggestions!