End it where the upper cabinets end.

All the way across to the end of the countertop?

Only between the upper and lower cabinets.

You wouldn't bring the tile across to the end of the counter? It just feels like such an empty space

I agree to end it where the cabinet ends. Then get a large piece of art to balance out that space.

Shelves are a good idea as well.

Here's a thought, be realistic for a minute.

When you prepare food on the counter, exactly how often do you splash food on the wall?

Probably once a blue moon, if ever.

Backsplash is meant for behind the cook top and behind the sink.

For the OP, she only needs it behind the cooktop.

Why waste money putting it where it isn't needed?

Confine it to where it belongs will not only save you money, you will be able to get a nicer and more costly tile and border tile ( half round or quarter round) to put in the space where you do need it.

floating shelf [or two] there embedded in a white subway tile...maybe some shade of warm gray grout. You have a bit more than expected vertical in kitchen with the extra tall cabinet doors all the way up to ceiling and the three large pendants at the end of kitchen . So I would take a plain but good looking tile all the way up to ceiling and all the way out to edge of peninsula counter. Just don't go overly bold, and figure out the shelf part [floating] so you know what you are doing w positions and your displays/objects. etc. You made a point w the tall doors and there are no glass doors /no molding to compete w tile....so keep on the same theme w tile. It'll look good in this instance.

Not really what I'm asking for, but thanks. I've already bought material, money is not a factor here. Just a design issue.

what do you like?

I personally like the tile out the end, but other prefer it to stop at the cabinet.

To me, it looks silly to stop at the cab w/this much overhang. (if it's only a few inches, fine)

I'd go to end and stop it under the top shelf.

basically like this, but your shelves would be here. you can choose to stop the tile like this, and install two shelves

stopping the tile under the first or even 2nd shelf

or tile all the way up. Which ever you prefer is the right answer

since your ceiling isn't that high, if you like it, take it up to the ceiling.

just please don't end your tile like this. get bullnose edged tiles or a Schluter Jolly