I am friends with the owner of Kiyoi, a locals only sake bar that provides small dishes that center around traditional (and modern) Japanese home cooking (done at a very high level)… this is not something you can easily have either.
This could be your last stop if you do an early sushi dinner or you could have your full blown dinner there. This is one of my most favorite places to go and I’ve visited six times (no joke). Love it to bits.
Tabelog page 喜宵 （㐂宵） - 神泉/日本料理 | 食べログ (don’t worry about the lack of score)
The owner unfortunately speaks literally no English (and there is no menu either) but if you let me know I can help you book and communicate with her in advance (I have ways around the barrier) to ensure she finds an English speaking employee (or perhaps her customer friends) to assist you and your wife when you visit. They only take reservations within the same month and basically announce who is on duty at the start of each month.
The owner did an interview for this online magazine and her words and story are translated to English
Though if you two prefer only high end options, L’Effervescence for Japanese French that is really really good. Book on OpenTable and if you can make it for lunch it’s even cheaper. Ask for Aoshima Sosuke who is the beverage director, his sake pairing is quite legendary too although you can mix with wine.
Of course you can always try Ishikawa, Goryukubo for that Hayato upward lineage if kaiseki ends up being the winner of the battle.