Where are you at? It looks like a place where it might be nice out year round. What is the black thing on the left- a gate or a screen or? It looks like there are hinges there so I'm guessing it's a gate, but want to confirm.

I might replace the wood picket with something that feels more like the square lantern frame and gate/screen. Like fancy wire, wrought iron, fretwork screening. And take it from the square lantern and around the corner, not just the one wall where the wood picket is.

A mosaic of glass on the sides of the stairs would be colorful and could be lovely. So could some pretty tile. I'd probably go for a warm white to creamy yellow for that alcove- maybe the blue on the underside of the stairs.

What am I looking at? Haven't a clue.

Mostly illustrating @beesneeds good suggestions:

Stairs would be safer with a railing (building codes would require that in the U.S.).

We need more pictures. It's hard to understand the space. Is the main view from the chair, and the part under the stairs, in deep shadow, so we can't see is what you want improved?