This may not be helpful at all, but I would go a different direction. I would pull out the flagstone and put in one of the big urns that is a fountain. Before doing so, you could put down landscape fabric to help with the weeds. Then I would put rock in the area or maybe some plants that will stay small.

This is sort of the concept but there are a lot of different kinds of urns out there to choose from.
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A quick fix would be to add pots of flowers. Looks like a shady spot, so maybe hostas. Something tall in the corner or on wall with hose.

Put a outdoor wall fountain against the wall

http://www.soothingwalls.com/outdoor-fountains/wall-outdoor-fountains.html

I love this nook. I would suggest that you put some trellis or lattice for height ( painted the same color of the house) up each side of the nook and grow a climbing plant that is appropriate for the light level in the nook; maybe a clematis or honey-suckle. This area also invites a lower round table in front of the chairs for a glass of wine or plate but also to bring the nook forward or out. Have fun!

White chairs, cushions to coordinate with front door. Nice round table with colorful potted plant on table.

If you want to keep the flagstone I would pull it up and add sand and then grit them in so no weeds. However, the fountain was my first pick or you could do a small koi pond.

I agree a fountain would be nice, maybe some ferns in pots around it if the climate is right.

I'm with Deborah Butler. I'd remove the flagstone and create a "garden". Split leaf philodendrum in the back,maybe some ferns and low annuals in the front. Maybe a small birdbath as a focal point.

Easy and inexpensive way, put an exterior rug there and a bench. It's welcoming.