I would paint them either white or grey.
The bigger issue for me, would be the angled double island, which is awkward and looks dated. I would replace these islands with one large square one, to modernize the kitchen and make it more functional.

That is an interesting idea, Patricia Colwell! Might be hard to insert cabinetry into the base, but the seating is very nice! S*

Not that bad any good cabinet maker can help the one in the pic has a straight counter fot he lower part where the cabinets would go.

Leave the cabinets and go for new paint on the walls.. Dark and dramatic. Reds, Plums or GREEN. Maybe update the knobs. You'd be amazed how much better they look with a darker framing.
Maybe a windowed cabinet door in the corners as well. (maybe) -something to break up like solid line.
Much less commitment than staining cabinets.

Paint the cabinets BM white dove and paint the island gray

I'm going to vote for painting a dark gray (or gray-green?) if you are going to keep the counter tops. They look too white to go with white cabinets. And I LOVE that curved island...wow! BUT, if you can afford to rip out what you have now, the dark paint and some snazzy new barstool/chairs will make a splash against the light floors.....do it in stages.

Are you keeping the countertops? What is your taste... traditional or modern? There is a lot you can do and it depends on your style/tastes. I agree with others comments above on replacing the island with something larger and more up to date in shape, whether it be square/rectangle or curved. By the looks of it, 2 islands could work as you have a lot of space. The first one could be more storage and prep with a secondary sink, and the second island could be the seating area with bar stools.

I have a lot of clients painting their perimeter cabinets white, while keeping the island a dark gray or wood tone. You can tie them together with a countertop that resembles marble or quartzite, or even pair 2 different counter colors. For example... black counters on white perimeter cabinets, and then a light colored stone on the island with more whites & grays. Here are a few examples of color combinations that would update it! (the last is more of a warmer feel):

Definitely thinking of changing the countertops to granite

I would change all your black appliances and do the stain oak finished.