Recommendations sought for Akasaka (Tokyo)

Hi all,
It appears that the Lovely Dining Companion and I will be going to Japan later this year. We will be staying in Akasaka and though we've gleaned some nice recommendations for Tokyo in general from other threads, I'm always amazed at the specific knowledge of people here. So I'm asking for recommendations specifically in Akasaka (or close by, which would include Roppongi). We are looking to be frugal (as distinct from cheap). My mother-in-law (born and raised in Japan) will be with us for some meals, so recommendations likely to please her as well are welcome. What I think that means is this: she is older (70s), not adventurous, more interested in "nice" (no, I don't know exactly what I mean, either) than great food (sort of exactly the opposite of us), and with perhaps with fewer or no tourists. Thanks.