Sushi Nozawa in Studio City. A few people say this place is overrated. But I thought it was the best sushi I've ever had, and I didn't know anything about the reputation when someone took me there. If you're a sushi fan you have to at least try this place. If possible take a friend who's never heard of it and see what they think. It's got the highest zagat rating of any sushi place in LA. I keep meaning to go back and do a real trip report with pics.
They call the chef who runs it the "Sushi Nazi". Supposedly he will kick you out if you try to order a California roll. Basically everyone just orders the special (omakase) and they start bring rounds of stuff until you tell them to stop (each round is charged).
Lots of tuna when I went, which is awesome for me. We let them go one round too far and couldn't finish our toro. The first round was some kind of tuna pieces in a tasty sauce that was unlike anything I've ever had a sushi place. It's the only sushi place I've ever eaten where the rice is warm, which seemed to make a huge difference.
The place looks like a hole in the wall, but is not cheap. Plan on spending $60-100/per. Also it's tucked away in a little strip mall, on a stretch of road where every strip mall has a sushi place.