I would continue to the end of the countertop (where you have the board) but tile below the countertop as well.
Where should the backsplash end?!
"Small kitchen design "
The Best Suited Floor Tiles: Porcelain, Glazed Ceramic or Vitrified
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I would recommend bringing the tile all the way to the door trim... and continue it to the floor. Something like this :
Take a look at this way to deal with ending a backsplash. Maybe you can incorporate something like this.
The wrong ending can ruin the look of your kitchen (yes, be scared)
I think Studio M's suggestion is the nicest way to tile that area.
Consider stopping the backsplash at the end of the cabinet and close off the tile with a piece similar to this. If you notice in the picture above the backsplash does not go to the end of the counter. Nothing is going to splash on that wall so it's more about aesthetics.
Here's a look you don't want.