Oura Onsen 大浦温泉 is small with a sea view in the north of Yakushima, near Isso.
Kusugawa Onsen 楠川温泉 is situated on the north east of the island.
Yakushima Iwasaki Hotel 屋久島いわさきホテルhas both onsen and rotenburo with all shampoos etc provided, but of course at a higher price.
Onoaida Onsen 尾之間温泉 is a very reasonably priced onsen and is probably the hottest on the island. You will need to take your own towel, soap and shampoo etc.
Onsen 温泉