Sukayu Onsen/酸ヶ湯温泉, traditional onsen, bus running from Aomori train station takes 1.5 hours until the Onsen. Before winter, one can also go to nearby Hakkoda Ropeway Sanroku Station/八甲田ロープウェー 山麓駅, and use the ropeway to a mountain. You can hike from there to the onsen. I got there end of November 2020, when the ropeway was already closed and there was snow - I walked to the onsen via road.
Aomori Museum of History, not far from Aomori train station.
Nyuto Onsen is an area with 7 onsen. I went beginning of December 2020, temperatures around 0°C. Most (all?) of the Onsen also are ryokan, one can stay over night. In December, some did no longer accept overnight stays. The traditional old onsen like Tsurunoonden (鶴の湯) are beautiful, but I would not want to stay in these traditional style rooms in winter.
I stayed in the “Komagatake Grand Hotel”, recommended. It has western style rooms, an outdoor onsen, offers breakfast/dinner. From there, one can walk to the traditional onsen, and stay as day visitor.
The Nyuuto area is a bit hard to reach. I arrived by train at Tazawako station, and walked from there in 4h to the hotel. A bus runs also, google maps has the schedule as of 2020-Dec.
You can go to the Oirase Keiryu hotel, and walk 14km to lake towada link1link2