I think those cabinets are cool, too, and I would not paint them! I would remove the uppers over the peninsula and probably the corner cabinet, too.

I’d try to improve the lighting. Is there a central fixture on the ceiling? Do you have undercabinet lighting?

If you remove the cabinets over the peninsula, which is generally an improvement, you still have the soffit hanging out in space. That might be weird. Also, judging by what's on the counter you need the storage space. [I like that you took a "real" photo of how your kitchen looks today. It helps.] Replacing the countertop and maybe the sink if you want a change is always nice, but is there room on the other side for stools? It looks like a doorway opens right into that space.

Some general thoughts on this kitchen:

It's really small with a less than ideal layout - for instance, the stove right smack next to a doorway. It doesn't sound like you're up for burning the whole thing down and starting over, so the question is how to improve what you've got. Changing the hardware was a good idea.

* I assume that some of the stuff on the counters is because of the recent move and unpacking, but even so, you need to cull your stuff. If you haven't used whatever in forever, get rid of it. If it's something you use seasonally/very infrequently find it a home elsewhere - garage? linen cupboards? Bathroom cupboards? Organize your cabinets so everything has a home, hopefully an accessible one.

*I can't tell if the soffit lighting is good enough on the countertops. If not, install undercabinet lighting.

*If the peninsula cab adjacent to the DW runs all the way to the wall, you could see about adding a door to the dead space on the back side of that cabinet. This would give you access you currently don't have and could be very useful. A door on the backside wouldn't even have to match what's in the kitchen, just stained to match the cabinet. (unless there already is one?)

*If the current countertop is in good shape and you like your sink, I'd leave them alone. Save your money for a future reno. Those cabinets are pushing 60 years of family use and won't last forever. Right now, they're fine, but all good things come to an end.

*Love the dog!

Try light your kitchen this way. Make a lot difference!

Replace and add lights; keep the dog.