Seems similar hue of both your floor and counter, clay terra cotta - cabinets maybe a softwhite/ creamy paint, something like this room --

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Idk if you can keep some cabinets, but the fronts look thick, real wood. Some would add an indigo or informal blue to island...

What a wonderful large space !!!!! And yes, it can use some help ...colors are blah as is but so are the doors of the cabinets ....the moldings are old fashioned and I would take them off for a sleek look ...then paint them a light creamy white . Then look again . Depending on your budget ..look at flooring ...maybe wood flooring, marble , terra cotta ? I would live with the kitchen after you paint it , to see what to do next ...I don't like the backsplash , but to start I would put a stainless steel sheet behind the gas range to cover that entire space ....then look again . Or , if you can afford it hire a kitchen designer and do it all at once . In order to tackle floor and changes in design and layout you really need to see a few architectural / design ideas in 3D and in color . This space is too large ...it has to be done right ...from the start or start of small and live with each step for a while doing it yourself ...and some advise from friends/HOUZZ ...

I thought the ceiling was spectacular, then looked again, and all I can see now are the white vents and smoke alarm! Any thought to whitewashing the ceiling, to lighten it up? Or at the least, painting the vents a brown tone pulled from the wood? I’d move the smoke alarm to a wall. At the stove, it will go off all the time.

OMG, what a beautiful kitchen! - And that stove!

Um, this may seem a little obvious, but I'd start by painting all those yellowish walls & soffits in some other color. Everdebz's soft creamy white looks like it would be scrumptious with that ceiling, or maybe a a soft periwinkle blue to tie in with that glorious stove.

Take a look at the recent " industrial inspired kitchen story on HOUZZ " you might find it could work in your GREAT space !!! Go slow and enjoy ....this space deserves you to look at all options ...!!!!!!!!!!

The good: the wood ceiling, the blue range, the granite counters, the wall of glass doors, the space
The bad: floor color, cabinet doors are dated and heavy, cabinet color, backsplash color.
If the cabinet boxes are good quality and in good condition, I would have them cleaned up. Replace the doors with something simpler.
Replacing that amount of granite would be a huge expense. It appears to be a mixture of colors, mostly brown...there may be white, gray, silver, cream and black included.
When I had brown granite, I selected a pale silvery gray for the walls: it works with the stainless steel appliances, the granite and the faucet.
I would paint the cabinetry a light color found in the granite, probably white.
The backsplash should match one of the lighter colors in the granite. I would use a solid color.
If you replace the floors, you may want to consider wood-look tile in a color similar to the ceiling.
I would repeat the blue of the range in countertop appliances and accessories such as kitchen towels, canisters, a ceramic container for large utensils, and some art.

I actually love Saltillo floors but I understand a lot of people do not. That has to be your first decision because removing that super thick floor will require removing all the lower cabinets first.

Removing Saltillo is one of the messiest priciest floor projects. If it goes under that wall of built ins you may seriously want to consider a design scheme that keeps them.

Budget will determine how far you go. Paint and backsplash would be the minimum.
https://www.houzz.com/photos/hanover-transitional-kitchen-dallas-phvw-vp~38494680

I love the pic Zmith posted and it shows how Saltillo can still be ‘current’ if you are going for a more rustic old world vibe. And as in my inspiration pic it shows it in the context of a more contemporary slightly glam vibe. Again, all starts with the floor and if it stays or goes. Curious to see where you go with it because I think the space has a great feel already.

Have the saltillo tile floors professionally stripped and sealed if they were not done when the place was for sale. Chances are good that they have yellowed wax on them now. They could be a lot rosier and pinker after professional cleaning to remove old yellowed wax. Their appearance will affect your new color scheme options.

Do you have a budget range in mind for changes or are you in the gathering ideas stage?

It is possible to have satillo tile stained a different color. That would open up the possibilities for your kitchen.

Lighter -

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Darker -

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Thank you all for the suggestions! We definitely want to remove the Saltillo tile and then take another look to see how the space looks with out the Saltillo.

We are concerned that the ceiling has a pinkish hue but it could just be reflection off the Saltillo yellow coloring. If we could we would love to leave the ceiling as is but I love the idea of painting the vent a darker color

Unfortunately, we cannot stain the ceiling due to a gloss that is currently on it. Seems like a lot of work to remove that gloss finish

If need be, we have budgeted to redo the entire kitchen from scratch minus the appliances

You have a lovely space with so much potential! If it were my kitchen, I would try to live with the floors (they don't look terrible on my monitor) and/or look into staining. I would paint the walls a creamy white and also reface the cabinets in a creamy white (and replace any door with arches with a more simple design like you have on your pantry wall). I would leave the counters and replace the backsplash, but I would get everything else in place before considering backsplash options.

Call me Captain Obvious (again!), but do you know when the ceiling was last cleaned? Years of residue from cooking could be affecting the apparent ceiling color. Even more so if the previous residents were smokers.

Your ceiling seems to have a thick and/or glossed finish - do you like it?