I would replace your current window treatment with a nice thin metal rod extended beyond the width of the window so that the curtain panels stay on the wall (take down the existing scones/metal ornaments). I would choose a large floral pattern perhaps corresponding to the color of your leather chair (dark red/wine) for the curtains. Some color and bold pattern will add a character to the room.

If you want help with difusing light and still wan to see out, look at Hunter Douglas Top Down Bottom Up treatments in Duettes or even woven woods.Treat each window individually. If you want to be able to leave your blinds down and tilt them so you can see what looks like a wonderful view, then look at Silhouettes or Pirouettes. They all come in colors that would compliment your room.
Once those are up, then you can see if you need to add stationery side panels.
Chrysteen

Lots of ways to go with this one. I'd hate to miss the opportunity for a window seat with storage.

Thanks so much for your suggestions. I really like the idea of an up-down blind, privacy and shade, though not sure I could picture it with drapes on either side. Also like the woven shades. Don't want to get into constructing a window seat. The flooring will be replaced with a medium ash within a year too, something else which may affect this choice. With the trim "cloud white" and wall a grey tone, would I go for white blinds/shade?