When designing a room I like to think of a real world parallel and start from there. In this case it would probably be a gym or dojo, right? So, there's the obvious training area, a big open space. There's also maybe changing rooms, showers, or baths? Maybe a place to sit between workouts? Since it's likely going to need a wide open space (you'll be saving on item slots) you can really get creative with structural things, too, like pillars and walls.
Also, this site, Housing Snap, is really great for inspiration. I'd caution against outright copying things just because that's not super nice, but it's a great place for inspiration!
Also, this site, Housing Snap, is really great for inspiration. I'd caution against outright copying things just because that's not super nice, but it's a great place for inspiration!