I noticed the post Cathy2 referred to is all about izakaya in the suburbs. I actually found it easier to go to L.A. for good izakaya eating - it was that hard for me to get out to the 'burbs (for a time, I had no car!)!
In the city itself, I know of no true izakaya, and although Oysy bills itself as an izakaya, it's really just another sushi place with a few grilled items on the menu (and not many). In Japan, the izakaya I went to didn't serve sushi (restaurants are a lot more specialized). Izakaya there are small places to drink, and serve grilled items mainly to accompany beer or sake. I'd love for a true izakaya to open up within the city limits, but what I'm really holding out for is a robatayaki!