If it was a chain and had free refills at a drink bar, it might have been Johnathon’s https://www.skylark.co.jp/en/jonathan/menu/index.html
There are a bunch of other one-off places as well.
No it was a small hole in the wall place in (I think) kyoto that had a single employee and like 4 tables. The walls were literally covered in Americana shit but heavy on the advertising slant (which is pretty definitive of american culture tbh)
It did have drink bar though, though not nearly as much selection what you’d see at a family diner type place or karaoke