How to finish a window installation

You could do this as an outside corner, with just a little piece of rail.

I did this with some baseboard right beside a closet (that I didn't want to put trim around), and it turned out well. (Taking this picture also reminds me, I never did quite finish cleaning this all up).

The hardest part of doing this is cutting the edge piece so you get a perfect corner.

1. Cut the piece (usually there's a scarp piece around that will work). Go longer rather than shorter.
2. Use wood glue or a construction adhesive (like No More Nails) and a clamp to attach it, with the edges meeting. Let it sit overnight to dry.
3. Sand off any excess glue that came out.
4. If needed, sand down the back side so it's flat (if you cut it a bit too long). A couple seconds on a belt sander is perfect.

That's really all there is to it. In your case, you may want to also sand down the front corner a bit so it's smoother, rather than sharp and likely to poke someone.

We had an almost identical situation in a former garage that we refinished to be an office. Our contractor suggested this and we liked the result: he installed a piece of wood about an inch out from the concrete, putting insulation between them and keeping the wood a consistent and level height - a little higher than the concrete. I can't remember if it was pink fluffy insulation or spray stuff. Then a shelf about 6 inches out from the wall - nice and level by being a bit up from the concrete and supported by the vertical wood, and there's insulation under the shelf too. The whole thing is a good looking clear pine and is well varnished.

Looking from the side gives an idea of the distance from the wall:

The shelf runs around the entire room and is remarkably useful for something so low. It hides all the lumpy bumpy aspects of the concrete and while it's not something you see everywhere, no-one has ever mentioned it so it can't be that unusual.