I would remove that odd looking trim behind the hand rail on the wall and add wainscoting on that wall. I would move the hand rail to the other wall. It can be secured to the stair post itself at the top of the stairs and then the bottom of it would be secured to either a wall or the bottom stair post. For a really dramatic statement a panelled treatment can be applied to the whole stairwell floor to ceiling using inexpensive molding strips. You can really change the feeling of your standard stair case in this way

Sometimes people hang a pendant light over a staircase like this. But otherwise, it depends on how much you're facing the stairs from the railing (looking at the blank wall) rather than just walking up and down the hall at left (not looking at it) -- in the former case, I might hang something there, but otherwise not. Also depends a bit on landing, etc....

A few ideas, not necessarily color?? But possibly a wall paper? Or a different color? Here's a few ideas???