There is an edge piece for this but we bought a metal finishing cap that matches. I'm still not sure if I should end them where the upper cabinets end or where the wall ends.

just try to do the neatest finish you can. is it a Schlutter® edge?

make certain it is level so it doesn't add another line to draw the eye.

I hope you are running the tile vertically and not horizontally as shown.

Why do you think it needs to go vertically?

Looking at your photos, a few thoughts from the building side. On the cabinet run, I would stop the tile in line with the outside edge of the upper cabinet, not at the end of the wall. With the metal cap you already bought, the narrow strip of painted wall beside it will read as intentional. Where the counter runs up to the door casing, take the tile to the casing and finish with a neat caulk joint in the grout color. On the wall without uppers, stopping at the height of the cabinet bottoms on the other side of the door gives the eye one continuous line, and a shelf makes a natural cap. Two build notes: the shelf needs studs or solid blocking behind it, so find the framing before you tile; and tile makes the wall thicker, so the outlet and switch boxes need box extenders to sit flush with the tile face (power off at the breaker first). The joint between counter and tile gets flexible caulk, not grout.

Rick Bozetti – Bozetti's Design + Build

End the tile run to be in line with the upper cabinet. Finish it off with a trim piece.

An overall pic of the entire kitchen will help with this decision. Context is key.