You have a few choices , treat them separately by using extended roods to make the windows appear wider , use one panel on each of the sides, or treat as one by covering that piece of wall in between.

You could paint the casings the same color as the wall, or perhaps remove the casings altogether to make the windows recede.

I like the mirror idea above. Or get a china cabinet for that space.

Put long window coverings on them (if you are going for a more traditional look) and a piece of art work in between them to give the room more personality. Or the more common solution is the mirror, that also works.

Thanks to all of you for your suggestions. I can see each of them as a possibility. However, as much as I like the mirror idea, this area adjoins the kitchen. Wouldn't a mirror treatment lend too much formality to such an area?

I would get a custom roman shade for each window,

These two pix won't seem to relate at first glance, but I think this will help you get the casual look you want. Build a third matching "window" between the two you have using the same trim for framing. Use mirror or frosted glass with a hidden light and switch, as seen in the first photo. Then install bamboo or other fiber shades at each window as shown in the faux window over the fuse box in photo number two. In daytime, turn on the light for the faux window and turn it off at night. You might even want a dimmer on it so you could match the light to different times of the day which would glimmer from behind the shade.

I don't see the problem unless your neighbor's house is Right There. I'd put top-down honeycomb shades or minimalist cafe curtains in them if need be, or just enjoy the view -- should be no problem in a dining room!

If you have a decent view why don't you put in a big window, get rid of the two little ones, since you're remodeling anyway.

Mirror would definitely not be my first choice....or second or third. Artwork gives the room so much personality and can make the place totally your own.

Hang curtains of your choice:

The point of the mirror is to have the whole space, window, mirror, window, mimic a larger window. But I agree, if you're remodeling, just have one big window put in.

How great to receive advice from such knowledgeable and creative people. Putting in just one large window is not feasible for this particular project, though I can see the virtue of it. Our view is very nice, especially this morning with sugar maples in all their glory. For the time being I will do nothing, and as things come together I will certainly revisit many of these ideas. Thank you!

Good luck Diane. :-)

I added a large window to my wall and love it, a picture window in the center and the end once open crank, out and got a roll down shade that you still get light coming in. I love it, I feel that curtains are to heavy, in my living room I got linen and light comes thru so pretty, I don't like dark rooms, specially since I have dark furniture and dark wood floors. Good luck !!

You have a lovely view! That big window was a beautiful decision for you.