Why not look for a lovely antique or a thrift cabinet you can paint in an accent color instead of a kitchen-type cabinet? You can use it to set up a bar/coffee station--this idea but small enough for your space and in a style that works with your kitchen.

While you are at it have the wall switch moved so you have more space and a better placement for the switch.....someone goofed.

I think a cabinet there would crowd the walkway.

I agree with Elizabeth B. I would leave the corner open. White/open space is important.

Have the children outgrown the little play table? If so, move it out if the kitchen, maybe out if the house unless you anticipate another child in the near future.
Do you use cookbooks? You could place a low bookcase there for cookbooks and even the kids’ books. It’s a good wall for displaying more of the kids’ art above the bookcase.
If you want/need a storage cabinet there, you could use a cabinet which matches your kitchen cabinets but is shallower than a base cabinet (12” up to 18” deep to hold canned goods, boxed items, serving pieces, or other supplies). The cabinet could be counter height with a counter matching or contrasting with your kitchen counters. It should be installed like a regular base cabinet, attached to the wall.

If you need storage why not a apntry cabinet with frosted glass doors for dishes and glassware since it looks like it is next to the DR.

If depth is an issue but you want storage you can do upper cabinets as lowers with a counter top on them. I have seen it done in a VERY narrow galley kitchen and it worked well.

Thank you all so much! We would really like some additional storage so I like the idea of a pantry cabinet or narrow/upper cabinets as a base. That way it won't the walkway but will meet our storage needs.

I think some child would argue that that is not dead space. At. All.

Big meany.