The Sawk-n'-Throh Dojo is a building where young Pokemon can train in Serenity City. It is owned by Sawk (and Throh), who seems to take good care of it. It is not only their dojo, but their home as well. The two Pokemon had various rooms behind the screen doors.
The main training room is where they spend most of their time. It is where you can find the trainees, as well, when it's open, of course! The room is pretty empty, because of dojo tradition. Normally Pokemon will be practice battling on the floors, or sitting on their knees listening to a lecture from Sawk.
The break room is where Sawk and Throh move to on breaks, for meals, or to talk in private. It is very restricted to students, for some reason, but it's just a very small room with a table, and some other furniture. Sawk disapproves of most of the electronics Throh brings into it, but sometimes the red 'mon can sneak 'em in there. You can see Zombie Forest through the window, due to being on the edge of Serenity City.