Should I leave the four inch backslash on those sides?

This is a tough one. I really can't imagine leaving any 4 inch backsplash anywhere if you are going to be removing most of it. I think it should be all 4 inch or none. So saying that you are doing a full backsplash which will be beautiful and functional, I would remove all 4 inch. However, you will likely have some drywall repair and the job of repainting those areas if you do not recover with tile. For example, I agree that the peninsula area should not be tiled. I don't believe it will look right. However, it will be hard to match paint and make that wall look seamless. It will take some work, although the finished product will be beautiful. I agree that I would just backsplash a straight strip behind the stove and not wrap around the side. It might look just fine to leave the unbacksplashed areas with the 4 inch, which would save a lot of work, but I just can't see it. One thing to consider.....If you do remove the 4 inch on the peninsula area and paint down to the countertop, it's hard to say what you will find. When installing countertops, the installers take into account the backsplash when fitting countertops into place. If it is known that a 4 inch backsplash is being installed, they aren't as precise when fitting the countertop along the wall because it will be hidden anyway. One last note....Although I am not a huge fan of the look, I have seen backsplashes added above the 4 inch existing backsplash, which would be the simplest solution. If you tiled a similar color as your countertop color, that could work. Good luck with everything.

I really don't like the way a 4 inch backsplash looks. It chops up the wall area.

The best way to figure out where a backsplash goes it to put it under where cabinets backs are attached to the wall. Don't turn corners and take tile to the edge of the counter. It almost always looks awkward. Finish the edge of tile with a pencil tile or you might find these helpful.

The bracket wouldn't need to be this ornate or thick if your kitchen is modern.

So the new backsplash should only go on the back walls behind the stove and behind the sink. You should remove the 4" everywhere else and not put tile there. I really like your kitchen.

These are all great suggestions! We will be painting all of the walls anyway, so I believe we may rip down the 4 inch and run the backsplash only behind the spaces you all have mentioned.

Anyone ne have any suggestions on colors? We were thinking White subway tile. What do you think about white against the beige?

The beige should look just fine with the white backsplash. But if you want a little change then now's the perfect time. I also like the gray- sage green in the middle picture I posted above. Don't know what it is but you're not tied to the beige. Keep it light and neutral.

For some reason, I don't see a white subway tile. I think subway tile would be a good style, however, as the style of your kitchen is very classic and subway tile is a good design choice. I'm concerned that the white tile will make the ivory cabinets look dingy. It may look great, but it's hard to tell. In my mind, I see a subway tile that is more in the light taupe family. I see picking a shade that is different enough from the cabinet color, not as dark as the countertop, but a neutral color that blends the countertop and cabinets together.