In Kumamoto city:
Batten no Yu （ばってんの湯）
Google coordinates: 32.775517,130.738206
Yes yes and yes. This place is awesome. Great water, great atmosphere, and the ganbanyoku is amazing.
Google coordinates: 32.736606,130.748806
Tsuru no Yu （つるノ湯）
This onsen is right next to KK Wing, so if you spend a couple hours jogging there, you can hit up the onsen afterwards. Awesome!
Google coordinates: 32.842268,130.7811
Google coordinates: 32.790319,130.776181
Yu Rakkusu （湯らっくす）
Google coordinates: 32.785304,130.702415
Shiro no yu (城の湯)
Google coordinates: 32.810975,130.701642
This onsen is very close to the castle.
Onsens outside of the city:
Kafutei Onsen（花富亭 温泉）
Google coordinates: 33.024209,130.780946
Green Pia Onsen〔グリーンピア温泉〕
Best view from an onsen. It REALLY is breathtaking.
Google coordinates: 32.801416,131.036976
Akagawa 〔赤川 温泉〕
Google coordinates: 33.053637,131.229237
Kikunan Spa Resort: Anganasse （菊南スパリソートあんがなっせ温泉）
Most classy, make-you-feel-rich onsen in all of Kumamoto. Go there once to feel like a king. It does cost 1400 yen though.
Google coordinates: 32.860425,130.727809
Tarutama Onsen （垂玉温泉）
An amazing onsen with a traditional feel.
Google coordinates: 32.862565,131.035672
Jikoku Onsen (地獄温泉)
This is a famous onsen. Famous for its mud. The main muddy baths are mixed, and ladies its ok to wear a towel in the water.
Google coordinates: 32.860204,131.036155
Possibly the nicest and most famous onsen town in Japan. People come from near and far to enjoy the wonderful atmosphere and onsens there.
Google coordinates: 33.078139,131.142039
This town has wonderful Autumn leaf viewing. Good to go here in the fall for onsen and autumn leaf viewing.
Google coordinates: 33.26607,131.368246
Google coordinates: 33.280028,131.507807
This is a hot sand bath town. The sand along the beach is heated by volcanic activity below. You can get buried in the warm sand on the beach, cook, and enjoy the view of the beautiful mountain ranges across the sea.
Google coordinates: 31.223078,130.655422