You have currently have a window where a door should be, and a purple door with red trim. There's no curb appeal to destroy. Put some more trash cans in front of it.

Your plan doesn't sound very attractive but maybe you need to do a sketch. Could you move the door back to its original location, fill in the purple door and put the range there with a vent to the outside over it?

What you describe does sound weird. Take the opportunity to re-do the outside while you are moving windows.

Because of the shelter above the window, It actually appears someone may have swapped the window and door locations. I'd remove the roof over the window and its supports and create trim for both the window and door that match painted white rather than red.

Budget permitting, consider creating a 6' deep concrete floor porch with a roof that covers both the door and window -- has the door and window centered beneath it. You could center the ridge of a forward facing gable roof for that or create something like this:

https://www.thespruce.com/porch-ideas-4139852

Thanks all. @latifolia, here is a photo of the entire back facade (taken before we painted the trim this summer), with the windows I am talking about photoshopped in (badly).

As for the purple door - that is just for fun, while we wait to replace the hideous white vinyl windows. When we do, the windows and doors will all be black or dark charcoal. We could put the door back under the portico, but unfortunately that would really limit the potential layouts for the kitchen, which I'm sure is why the previous owners moved it. The portico actually comes in very handy for keeping my smoker out of the rain, so I'm not opposed to leaving it as is, I am just wondering if there is an attractive (or at least non-offensive) way to frame a very narrow window inside what was obviously once a door opening.

Have you talked to a kitchen designer? Often a good one will come up with ideas you may not have considered.

Another idea would be to consult an architect about putting a porch across that side of your house. Is it a single family home? Is there space there to add on?

We haven't talked to a kitchen designer yet, but I have gotten a lot of excellent suggestions from the folks here (including some pros). The problem with the old door location is that given the internal foursquare layout, the kitchen connects to all of the other rooms only at the point kitty-corner from the old door, making for an awkward path across the kitchen to get to the rest of the house.

It is a single family home, but because it is built into a hill, there really is no room for a proper porch on the back. We have an 8' deep concrete patio that butts up against the first of several retaining walls that form the structure of our backyard. That retaining wall could be pushed back, but it would be prohibitively expensive.

@suezbell, we have considered adding a porch roof over the back area as you suggest, but it would make the back two rooms (kitchen and dining) very dark. The house faces west so the kitchen has north and east exposure, and with the portico over the east window it is already fairly dim in there. I was hoping to get more light in there with additional windows and/or a French door.

Definitely remove the portico if you are going to change the windows so dramatically. @suezbell has some good ideas.

Have you considered adding a flat or nearly roofed pergola or with green house roofing?

https://www.pinterest.com/pin/481463016415483665/

You could even create a shed roof back porch with greenhouse material.

@suezbell, thanks so much for those ideas. We have talked about putting a pergola across the back (though not with the clear greenhouse material, so thank you for introducing me to that!), but we felt like removing the portico and repairing the stucco, etc., was probably more trouble than it would be worth. However, if we are going to be changing windows and doing stucco repairs anyway, that would be the time. We wouldn't be able to extend it all the way across, though, unless it were quite tall, because the stairs leading down from our parking area (they lead directly to the portico) would require some headroom. Still, something to think about if we decide we want to change the windows drastically.