I finally made it to this very hidden place in Japantown, and since I wound up having things very different from the only other Kappa post I could find, I figured I'd give a report.
First of all, there is no other place like Kappa in all of San Francisco. When you walk in it's like you're in Japan. A friendly couple runs the place -- the wife is hostess, the husband is the chef. The clientelle is almost exclusively visiting Japanese businesspeople (businessmen). There is a counter that seats around 10, and only one small table. The style of cooking is "koryori" which means little dishes -- most of them cooked or marinated -- and the way to order is to get a bunch of them and share. The menu and specials are in Japanese -- the English menu only has basic items. They do not serve sushi, though they do serve sashimi (I didn't have any, however). I had heard that Kappa was outrageously expensive; It's very expensive, and maybe cost/performance-wise you can do better. But I wouldn't go as far as outrageous, given that there are things here you will not find anywhere else. Many of the dishes are the chef's own creations. For two the tab came to $115 before tip, including 2 large beer bottles. I ordered:
Myoga special - thinly sliced myoga, a Japanese vegetable that is like a cross between ginger and onion, topped with dashi flakes
Yamaimo sengiri bainiku ae - julienned yamaimo (Japanese tuber that has an interesting gooey texture when cut) topped with pickled plum paste
Kinpira gobo - traditional dish of simmered gobo (burdock root) and carrot
Shiso miso maki - miso wrapped in a shiso leaf and lightly grilled
Hirame shiokonbu ae - Pieces of raw flounder mixed with strands of salty konbu seaweed.
Hitokuchi katsu - "Bite-size" (actually each piece took 2-3 bites) tonkatsu (panko-crusted fried pork)
Mushi tori asapara miso ae - Boiled chicken and asaparagus in sesame sauce
Aji ichiya boshi - grilled aji (small fish) with grated daikon
Shake Ochazuke - Rice/sesame/nori flakes in tea/fish-broth topped with bits of salmon
Everything was superb, except the boiled chicken and asparagus, which was just ok. Standouts were the Shio miso maki (I love shiso, and this was one of the most interesting preparations I've ever had), the grilled fish (aji ichiya boshi), and the Hitokuchi katsu. Someone posted a while back asking where you could get great tonkatsu in SF, and I replied that I had not found great tonkatsu in SF. Now I have. Aside from the ochazuke, these are truly "little dishes" -- small, Japanese-size portions. But they add up, and I left feeling very full.
This place is obviously a challenge for non-Japanese speakers/readers. I asked the couple if they welcomed non-Japanese speakers, and they said they did, though they acknowledged that the language barrier could be difficult to overcome. The wife suggested that the $75 tasting menu could be a good solution, though you can certainly get a lot out of Kappa without spending quite so much.
While I was there, I saw her greet a non-Japanese couple with a warning that Kappa doesn't serve sushi, and the couple left. If you want to try the place, don't take her warning as unwelcoming -- just let her know that you have heard about Kappa and want to try it. Her English is actually pretty good too, and she seemed like she would be happy to educate eager customers willing to learn. The atmosphere is pretty restrained inside -- even by Japanese standards -- so if you're on the respectful/not-loud side, that will also help smooth the way.
There is no sign for Kappa outside. To get there, you go up the stairs in front of Denny's to the second floor. There is a sign on the door for "Club Nishiki," which is a bar next door. Go inside, and directly in front of you will be a sliding door with a lit sign above it (it says Kappa in Japanese). Slide open the door, and you're in. They accept reservations: 415 673-6004.