Perhaps blue glass tiles similar to the wall color currently there.

grey and white glass tiles are also popular

Either of the above would look really good. I'd keep it light colored and, with the shiny counter, maybe a matte finish could work. Bring home enough samples to really get a good idea. Love your floor with the cabinets and counter. Good luck.

I love that blue...and I understand you want something...but...every kitchen does not need a back splash...think about it...

We love the blue but we do need a backsplash at least by the sink and stove otherwise we will ruin the drywall.

I was thinking of the marble look since it seems to be the opposite of the floor tile but my wife is not feeling it.

What about stainless steel? Too much? Or a mix of stainless and tile?

The large BS tiles in this pic would coordinate with the tiles of yr kitchen floor.
Even tho you don't prefer small tiles you might reconsider after seeing the small tiles in this pic as it breaks up the expanse of the backsplash
ref pic

You might want to consider back-painted glass. It would be a clean, simple, and ultimately changeable, option. The backsplash area is measured by a local glass/mirror company and the back is painted whatever color you want!! These are nice for many reasons. They are affordable, easy to clean (smooth), and beautiful!! (type it in on Houzz to see examples) You might consider just doing above the sink and stove areas?? That blue color is really nice next to the white; it would be a shame to cover all of it up.

I like dawnmarilyn's idea. Glass would be really cool.

Can the glass be a matte finish?

Agree with above posters. Endless color choices with back-painted glass, no grout to clean. Very cool!

Maybe this? I know it is small tile but it doesn't seem too busy like one with contrast.