The Mei Getsu Gi in Kawanishi is such a place. A bit of a hike to get there from downtown but a memorable place with a great view.
http://www.meigetsu-hgc.co.jp/omo.html
Sushi in Japan is a rather casual food and mainly a filler in case you are still hungry at the end of dinner or for lunch.
"Sushi isn't the only Japanese food and I don't often sit on tatami to eat sushi."
Taxi ride downtown to ITM in early morning before 7AM should be pretty easy, 30 minutes at the tops.