Uminole/ Umi no le
I went last May. For $35 the chef will cook for you, and I had:
broccoli rabe, pumpkin (nice)
tofu skin, eggplant
mapo tofu with rice (very generous portion of Japanese rendition of a Chinese dish, imaginably something a Japanese mom might cook for their children)
signature pork belly with broth and mustard (very nice, this sealed the deal)
udon that resembles linguini in broth
It was definitely different from typical Japanese that we expect, literally stuff that a random, regular person might make at home, except that a real person might screw up something whereas at uminoie the pumpkin is slow-cooked to mushy and sweet, the fried tofu is exactly what it is, the pork belly melts in your mouth, etc. Don't get your hopes up though, the above dishes are very very humble and would be something you eat after a long day at work etc, maybe not what you would eat to celebrate something. I haven't tried the a la carte menu, but it might have less mundane-sounding items.
Also Tsukushi is $60 for a 6-dish dinner (you can add on more items) and is kind of "dive bar" food, it's a nice way to have a relaxing evening provided the price is tolerable. The cooking is more sophisticated than uminoie, for example they always have a sashimi dish.
I also like Aburiya kinnosuke which is $30-ish for lunch, and then much more like restaurant food, and so more "accessible" than the above.