Ok. I was born to answer this question, and you have described my favorite foods in LA.
Ramen: Daikokuya. Done. Best in the region.
Sushi: Sushi Nozawa. It was the highest rated Zagat restaurant for a while (even though the decor was like an 8 or something). Best fish in town.
Korean BBQ: Shik Do Rak (House of Duk Bo Sam). Yum.
Mexican: You can go a bunch of different ways (since the Mexican in LA is superior to anywhere else). Either slightly upscale at Loteria (on hollywood or in the framers market), or you can also go with nearly any of the taco trucks. Also, I’m quite partial to Tere’s Mexican Grill.
Artesia is really good for south indian food (Woodlands resaurant), though the last time I was there the food was less than spectacular.
Also, best cocktails in town: Hungry Cat.
Let me know if you need any more recommendations. I have many more.