This is a large jjimjilbang and sauna right on the harbor (Western, Seoho-man, just off Jungang-ro Street) in Tongyeong. If you are near the market and the replica of the turtle boat, it is right there. I'm sorry I haven't got more specific directions, but there's a wikimapia to help! I went on a Saturday around 1 pm, but it was not crowded at all and pretty quiet. The only busy part of the place was exercise classes going on on the floor with the weight room.
I saw many jjimjilbangs in Tongyeong and there may be better ones out there, but Haesu Land is a nice place to spend some hours if you are waiting for the ferry to one of the outlying islands. it is maybe a 10 minute walk from Haesu Land to the ferry terminal.
*Fun fact! When I googled Tongyeong Haesu Land (in a vain search for photos), it comes up as a wi-fi hotspot on the GlobalRoaming website! :)
117-5, Hangnam-dong, Tongyeong-si, Gyeongsangnam-do
Open 24 Hours
Jjimjilbang 10,000 won
Sauna only ~7,000 won
Wikimapia of Tongyeong Haesu Land