I have about the same thing in my house!
The stair case is off center, so I walled off the smaller side and added a custom door as a storage room.
The space is 6' at the center and about 12 - 14 wide. my two boys use the larger side as a bedroom / game room for their video games. We got them bean bag chairs and I built short platforms for their beds.
Unfortunately, we only let the oldest boys stay up there. The younger kids are a bit more timid! (We adopted 5 of our foster kids) Now, they are getting too tall for the space and we are looking at moving south so we can get a bigger house.
The room has served many purposes while we have been here and was even our bedroom while we were fostering. I'm 6' tall and I can't tell you how many times I bumped my head or pulled a muscle just getting out of bed for work.
Overall, I would just stress knowing your limitations. I've carried many dressers and bookshelves up there at my Fiancés insistence that they would fit, just to carry them back down, cut the legs off or do some other insane customizing.
My best suggestion,
Carpet the floor, put a flat screen tv on one of the end walls, get a few of those foam things that change from a chair to a sleeping mat and use it as a comfy video game room, a small theater for watching movies or just a convertible spare room for last minute guests.