Your kitchen is beautiful. I think it would be dramatic to tile the whole wall. Since you are doing white tiles it would be a clean look.

full wall looks lovely but can be very acoustically lively. i'm fine with ending it at the left cabinet as it looks like there is more wall than counter and the last inch would look indecisive, height-wise at the bottom of the vent.

My advice would be to tile the whole wall. At the side vertical edges include a tile edge finishing trim in a metal finish that matches other metal in the the kitchen.

Tile the whole wall

I think you could tile as high as the bottom of the hood and straight across on the left to the wall and straight down from there. I'd leave the lower left section untiled. To the ceiling is a nice idea, but I think you'll run into problems with the hood and paneled ceiling.

You don't need a back splash as there is no sink. You do want some protection for the walls behind the stove.

Think about this suggestion: paint the walls the same gray as the cabinets. Then tile the stove area, but do a the white of your counters for that area only.

The reason I am suggesting painting that wall dark, is everything is off center. Dark on dark will minimize it.

I agree with everyone who says to tile the whole wall.

I disagree with most: to tile the entire wall as an accent wall would be a bit much. At the very least I'd stop at the bottom of the stove hood which, conveniently, is level with the center horizontal seam of the overhead cabinets.

On the left there is a short wall above the countertop maybe 8" above the countertop and creating a short horizontal ledge -- about a foot long.

I'd either tile up to the height of that foot long horizontal ledge; or

I'd tile just one tile all the way across the entire length of the countertop as a trim and to prevent spills from going against the drywall and down behind the countertop,

If you can find tiles you like that, with one tile, reaches the bottom of the board atop that short horizontal ledge, all the better.

Then I'd protect the wall above the stove top.

I'd either also tile between the overhead cabinets from that accent tile up to the bottom of the stove hood or, better yet,

I'd get a stainless steel shield for that wall immediately behind and above the stove top -- the plain ones are easier to clean. If you choose a stainless steel shield for the wall behind the stove hood, you could even leave a skip in the horizontal trim tile and have the shield cover from the countertop all the way to the bottom of the hood.

On this shield, no skip in the tile was left:

http://www.hgtv.com/design/rooms/kitchens/stove-backsplash-ideas

On this shield, a skip was left in the single horizontal row of tile:

https://s-media-cache-ak0.pinimg.com/736x/f0/92/36/f09236e18ee52389e3d0d70b987cca32.jpg

http://s98.photobucket.com/user/twoyur/media/Picture018.jpg.html

On this shield, no tile was used -- only stainless steel all the way up to the cabinets.

http://www.quickshipmetals.com/quickshipmetals_kitchen-backsplash-long.jpg

https://lh3.googleusercontent.com/-wYnPYIVrUxI/Um-rPcqwTwI/AAAAAAAAAFo/nyMVd3zRdlc/w454-h231-no/kitchen-backsplash-glass-tile.jpg