The great sushi place you are looking for is in Otaru.

One day for Noboribetsu Onsen is fine. Go to the onsen bath at Daiichi Takimotokan and you will get a great view of Jigokudani. IDK the pond or the etc. You can stay at Takimotokan - large hotel with western beds, kaiseki dinner and a couple of restaurants. The basic idea is that you check in to your lodging go for a soak and then you put on the yukata etc and geta and clog about the town looking in the shops. Maybe visit an onsen bath at another location. Then go back 'home' for dinner and maybe a soak or massage or both So it is a get there mid-afternoon for check-in and then leave town next day after check-out.

I would take the train to Tokyo just to ride in the tunnel to Honshu and then blast on south from Aomori on the fastest shinkansen. Get reserved seats in advance, definitely.