In Tokyo, Kiyoi in Shibuya is a must try if you want to have sake with small plates focusing on home style cooking along with very classic Japanese bites and some items you’ll find at izakaya. They don’t speak English though and you’ll need to make reservations (better to do so through instagram, owner will find a friend to translate and get back to you)
Must try also: Chinju No Mori Animism Bar. https://chinjunomori.net/
Some more info here: https://pocket-concierge.jp/en/restaurants/244184
To book, do it through the chinjunomori.net website (send email but use lower case lettering). You may want to take their sake and/or Japanese spirits tasting class also.
If you only have time for one place, I’d say do Chinju No Mori for the top of your list.