Here's a great place to eat, not that expensive, and they get extra points for having a waiter on staff who happened to be standing outside when I arrived, saw that I did not have a lock for my bike, and so went inside to get one for me and then tied my front wheel to a pole himself. It was a combination lock so he had to unlock it upon my departure as well. (He had to come outside anyway to tell our group to hush as we were talking quite loudly and disturbing the neighbors.)
Our set menu consisted of some sesame tofu, a bit of unagi-tamago roll and pickled veg to start, fried yams with lemon and fresh cabbage leaves and a tasty dip, assorted sashimi, pork dumpling soup with a delightfully crunch chili-oil (we think the crispy bits were toasted garlic), onigiri, and for dessert, a slab of lovely vanilla ice cream inside a round of maple-sweetened crusty bread (unexpected, and delicious).
How to get there: if you are traveling along Roppongi dori, away from Shibuya station, turn left down a quiet narrow street (it's actually two one-way roads -- follow the direction of the traffic) a few meters shy of Gaein-nishi-dori (if you get to the big Gonpachi on the opposite corner, across the intersection, you've gone too far).
Once you've turned off Roppongi dori, continue along for a few minutes; the road will curve slightly to the left but you're basically staying straight. The restaurant will be on your left-hand side, in a two-story converted private house on the corner. Not much signage, just a small paper lantern and tasteful bamboo decorating the outside. Look for the signpost announcing that you are at 2-20 Nishi Azabu (address is 2-20-1).
I think the Bento.com review sums it up well:
This is a comfortable neighborhood izakaya that serves terrific food. ...with decor that veers toward the traditional end of the scale. Traditional, but never stuffy - the friendly, upbeat staff set the tone, and their enthusiastic shouts and the celebratory sounds from the upstairs party space create a lively auditory backdrop.