If I had a beautiful bay window like that, I would keep it and put a bench in front of it so I could rest in between cooking or have people sit and visit with me while I cook. You have enough room for a narrow island where you could put the sink facing the window if you want to get into moving plumbing.

rantontoo is probably right, the kitchen would be more functional without an island. I have barely an 11' deep kitchen so know how tight it is. I do wish I had seating in the kitchen, though, so there's that consideration. I have a bump-out window that could be called a mini-bay window in front of my sink, and the curtain over it is hard to reach and operate, and the window and bay shelf in front of it rarely gets cleaned due to the distance. Keep in mind the ease of cleaning that bay area if you block it off with a full 24" deep countertop.

The bay window is old and leaks air right now. It will need to be replaced and we currently have so little counter space. I am not opposed to putting in a new bay window, but a regular window is fine too.

Seriously consider 27" or even 30" deep base cabinets to expand your countertop space. It doesn't sound like a lot, but it will really increase the area you have to work with. You can combine a 27" deep base cabinet with 16" upper cabinets - though there are some really tricky requirements to do anything deeper than a 13" deep wall cabinet around a range top within certain parameters. Check the specs on your range if you want to consider that. To save on cost, you can also take a standard 24" deep cabinet and mount it further forward with lengthened side panels, but take into consideration matching expanded base depth with the wall cabinets. We're planning to do this in our kitchen that is almost your same size, and I sympathize on the limited countertop space. We also considered a rolling butcher block cart to help give us some small island space but are leaning more towards bigger base cabinets now.

It looks like the bay window is the only source of natural light in the room. If so, keep in mind that a room with flat windows on only one side will end to have harsh light, glare, and deep shadows. A bay window acts to bring in light from more than one side, mitigating that issue some. If you replace the bay window with flat windows, can you add another window on a different (hopefully perpendicular, not parallel) wall?

Inspo - I like the idea of deeper cabinets to get more counter space. I will definately look into that.

Isaac - We are planning on opening up the wall to the right in the image. That connects with the living area, which has a few windows. Hopefully that will help brighten up the space.