You could hang a new mirror above the built-in dresser. The cart with plant on top isn't right for the tall, narrow space it's in. What you put in there needs to echo the shape of the alcove. I love your archway!

Would you consider building some new trim and shelving into the alcoves?

Shelving in the same paint color as the wall in the tall alcove. If you don't wan to put a mirror back over the built-in I would suggest a large piece of art (photo or painting)

I like the idea of painting the built-in white and do a large piece of art over it. Then do wood shelving from floor to ceiling in the other alcove. Similar to this:

Try an image search for "built in alcove shelves" to get some ideas. Just installing simple shelves will be easy. You could get fancier and hire a carpenter to do something more involved too.

Elizabeth Forrest Lambert, I now agree with the other advisors: my suggestion of a mirror wasn't good; it would only make the alcove look deeper. Painting the built-in, as others suggested, is a great idea, as is the idea of built-in shelves.