Best Okinomiyaki in LA?
I don't know the places Downtown, but I can highly recommend Teppan Kamizidori in Torrance (far Northwest corner of Crenshaw and Lomita, on Lomita side). They have very good teppan dishes, but I always order an okonomiyaki as part of my meal. The service is good and fairly fluent in English, and the prices are very reasonable. The name means "wind indicator," and the picture of the weathervane on the sign is visible further away than the lettering itself.
I can give you a hint regarding finding okonomiyaki - if you see a Japanese restaurant that ends with the suffix -an, it is likely to have Osaka style food, including Okonomiyaki. The style is known as Kansai-ryori, for the area of Japan which includes Osaka. The -an ending is Kansai dialect for "tavern that serves food." (Osaka has a distinctive local dialect that is quite different from Tokyo Japanese - the toast generally rendered in English as "Kampai!" sounds like "Gambei!" in Osaka. Tokyo residents think this makes Osakans sound like hicks - there is quite a rivalry between the two cities. But I digress.) The best example of Osaka cuisine in LA, Dojima-an, closed a while ago after a botched expansion. They had the best Japanese seafood I have ever had in LA, bar none. If anyone knows a good Osaka-style place, please tell the rest of us!
You might try Takoyaki Gen at 327 E. First Street in Little Tokyo. Very plain decor, but you can sit at the counter and eat your okinomiyaki off the grill.
It is the only okinomiyaki place I know, so I too await more responses to your question.
Tombo in Torrance is by far the best okonomiyaki restaurant in LA area. It's the only one I know of that you cook your own. The one downtown is good, also. You don't cook it yourself there. But they do have hot chili's. Tombo is the only place I know that has munja. I have been going for many years. Jonathan Gold lists it in his book (if I remember correctly). He has written articles about it.