Chugoku Matsue, Shimane
Tennen Onsen Yuya Tenjin
天然温泉 湯屋天神
Name in Japanese. Look for this on the sign, or show it to a taxi driver.
Allowed with conditionsStated by the facility
Hot-spring bath. Hot spring (spring details not checked)

Tattoo rule
Allowed with conditionsStated by the facility
What the official page says
タトゥーのある方は、タトゥーシールで隠せる場合に限りご入場いただけます。タトゥーシールは番台にて販売しております(1枚500円)。
In short: Tattoos must be covered with the facility's tattoo stickers (500 yen each, sold at the counter).
Where it is
Chugoku region, Shimane prefecture. About 130 km in a straight line from Hiroshima.
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Rules can change. Check the official page on the day you go. Any paid link is labelled next to the button. We have not visited this bath ourselves.