What you do would be based on needs. Do you need shade? ... Privacy protection from overhead? Either of those could justify a pergola/arbor.

Based on the picture, the least attractive thing about the space to me is the white gravel mulch. A small space like this would be greatly improved by having a nice floor ... brick, pavers or decorative concrete. Could hold a couple of small chairs and a chess table.

The small space offers nice opportunity. I concur with Yardvaark that brick or concrete are nice options to create a small enclave for you. The attached photos show what I did on the side of my home which is 9' from house to fence. That appears to be a bit more space than what you have but the concept translates into your space just as easily. A small café table, a couple of chairs and some containers with annuals and you will be all set.

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K&D, that's a great inspiration picture for this project. Very nice looking!

Thanks Yardvaark! :)