I think it looks pretty and warm. It might be a trick of the camera angle, but your island looks a little tight to the sink counter. A backsplash would be pretty, but it should be simple with wood cabinets. I have a simple cream subway tile backsplash with my (older than yours) wood cabinets and I am very happy with it:

https://www.houzz.com/photos/my-pics-work-in-progress-phvw-vp~109854040

Perhaps a pretty roman shade or other window treatment?

This is not a bad space at all. My first thought is that the room looks dark. You could add some led lights under the cabinets. You could also brighten the whole room by painting the upper cabinets white. As far as back splashes go, a stacked stone would add some nice texture and you could even carry it up above the cabinets for a nice accent. Some other details that could help add character are updated light fixtures, cabinet pulls, and a new vent hood.

In addition to others' suggestions, a brighter colored rug under the table.

I think this is a very pretty kitchen, but a little more light would help. On your bookcase end, you might consider painting just the back wall of the bookcase a light white/cream... whatever goes with your color scheme. LED lighting could be attached to the upper portion of the bookcase to brighten it up also. I had a bookcase end like this that I turned into a wine cabinet (super easy) and added an LED light above. Of course, that only makes sense if you like wine :)

I like the idea of a light white/cream beadboard backsplash, runnng on the horizontal.

I think a brighter rug, as suggested by mjconti is a great and inexpensive update!

Do you find the room to be too dark? If so, LED rope light above the soffit trim, and undercabinet lighting (as suggested by Kate).

These would all be inexpensive updates.

Any suggestions for a rug?

I think you should look for a rug with a lighter background colour and has the colours of your island and different wood tones, something like this one but it may not be a match with the island colour. Then I would also add a Roman blind in either a solid or pattern that’s predominantly the island colour.

Are you considering a new kitchen remodel? Or do you just want a cosmetic change?

J Design Group | Interior Design company in Miami, FL
225 Malaga Ave
Coral Gables, FL 33134
Ph: 305-444-4611
https://www.JDesignGroup.com

Lighting and a backsplash for sure.

When choosing a rug for under a table, consider if it is easy to clean, are there children that sit and eat at the table, etc. Then you can decide on colors for your rug - you may not want one with a light background for under a table! I've seen a few Mohawk brand rugs that are colorful stripes, no light background.