Regarding Tamagawa onsen and Nyuto onsen. I have been to both, and they are very different.
Nyuto onsen are some onsen in a green part of the mountains, relatively close to Tazawako. You can visit many different ones in one day (there is a day pass I think to visit 3 different ones). Some are quite touristic (e.g. Tsuruno yu), others less so. All are quite easily reachable by public transport or transport from the onsen themselves. These onsen in general are more for relaxing.
Tamagawa onsen is together with Shin Tamagawa onsen (just next doors, same water) are visited by Japanese for therapeutic reasons. The water is also totally different. It is at pH 1. I liked it, my husband could barely stand it (there are some diluted ones as well, where the pH gets up to maybe 2 or so. (pH 1 is like lemon juice from an acidity level). The onsen building at Shin Tamagawa onsen for me is like a wooden cathedral to onsening. Only the rotenburo part is not special (while in Nyuto onsen it is all about rotenburo). RIght behind Tamagawa onsen, you can (and if you go absolutely should) go and see the origin of the onsen (essentially boiling acid coming out of the ground) and people are lying on nearby stones that are hot from the water, are supposedly radioactive and the air is filled with sulphuric gas from the volcano outlets. When we went all the places to lie down on the radioactive hot stones had gone, and frankly for me the sulphuric gas was too much. But it is a SIGHT!
When we went to Tamagawa onsen, we had a car and made a day trip to Goshogake onsen https://www.japan-guide.com/e/e3654.html
and Fukenoyu onsen https://www.japan-guide.com/e/e3660.html
Both were amazing places. In Goshogake onsen we didn't go in the water, just walked around and had a look into all the mud volcanos. You can stand a meter or so from some of them and see them bubbling with boiling mud. See the earth at work. Up in Fukenoyu onsen, you can then bath in these muddy (and a little bit cooled down waters). There are segregated rotenburo but also a mixed one, which I would suggest. It is just in the middle of nature. And you sitting in the muddy waters from a nearby mud volcano. Very different to any other onsen experience.
I think from all my onsen experience in Japan, I would say Fukenoyo (for the mud and nature), Shin-Tamagawa onsen (for the cathedral like wooden building and the acidic waters), Osorezan (for the setting just in front of the temple on top of a volcano) and Kuronagi onsen (https://www.japan-guide.com/e/e7575.html
) in Kurobe gorge (for the nature around and the monkeys playing in the river below)... have been my personal highlights for onsen.
So yeah, depending on how much you are into onsen, you should not give a miss to Tamagawa onsen. It's a unique experience. Very different from most other onsen in the world. Probably actually unique.