wow... quite a challenge! Is the space to the left of the railings with the roof vent and trash cans or whatever they are, yours as well? If not would you be allowed to put up something to screen that view? I'm thinking of something like bamboo roll fencing (which could easily be taken down again later).
then at the bottom of the picture there's a sort of walkway and something that looks like a ladder on its side, then the asphalt or tar paper area. How easy is it to step over the ladder thing?
And you still need to give us some idea of the dimensions of this space.
Inspiration pictures always help. Do an image search on ideas for very small patios.
Here's a couple I found that way:
Think about white washing that back wall (if allowed) to lighten the space up. Think about decorating it. Think about building a bench along that wall so you could sit looking away from it. Think about putting down a thick layer of light colored gravel/rock over the black asphalt/whatever. It will also lighten up the space, reflect more light up to whatever potted plants you put there, and keep the roof from absorbing so much heat.
So on the right hand edge where the little potted plants are, it looks like it is a drop off on the other side? I might think about putting a row of potted hedge plants all along that side. If you look at the sample photos above, a lot of what makes them appealing is the sense of enclosure - a very private, secluded, safe little nook. Your space is small, but so far doesn't have that because of being open on both sides. Closed in, with lots of potted plants, seating area, etc it could over time become a very pleasant little space.
Is there electricity available there for a fountain pump? Some kind of little water feature, either a wall fountain on the back wall
or any kind of small water feature tucked in a corner amongst potted plants would add a lot of ambience:
As these show, you can do the small pond in barrel without a fountain, but it takes knowing what you are doing and careful maintenance for it not to become an algae filled mess.
Welcome to the Forum! Do be sure to keep before and after photos for yourself and share with us!