I'd probably put a buffet table or something similar along that short wall? It would help fill up the space but I'm not sure it'd do all that much. Google "buffet table furniture"
Otherwise I might just put a breakfast bar there with some stools? It'd be an alternative to the dining area?
Perhaps you could move the dining table into that space and put something else over there near the windows, like a collection of house plants?
I'm not very good at this, these are just my ideas!

Hi thelees, I think you have space for a pair of chairs with a reading table & lamps to make a little relaxing spot. Or you can put some book shelves along the half wall to store cookbooks or other reading material.

I agree with Bond Girl, I would use that space as the eat-in - the large windows in the other space make it a perfect Solarium - you could use some comfy furniture for reading and having coffee in the morning.

BG and BTSH above seem to have the right on! Here's an idea...

This is why I love Houzz! Thank you all - I'm loving the idea of swapping the rooms. Jaimieson, thanks for the link - the wheels are turning!!

I would have built-in shelves to match the kitchen cabinets install along the half wall of the stairs. With several chairs placed beside the shelves this can become a reading area. If you decide to relocate the breakfast room in this area the top of the shelves should have the same countertop as the kitchen and will function as a searving area.

You could also have a desk built into the shelves to creat a study area, computer area, for the kids.

Lately I have been adding comfortable ,loungey seating to some larger kitchens. You could do an oversized chair with a floor lamp. You should have plenty of room.