How much are you prepared to spend? Any person advertising himself as a cabinet painter on Angie's List (at
least, in my area) is actually a cabinet re-facer and s/he will spend a
long time convincing you to replace the doors and coat the cabinet bases
in some kind of film that is the same color as the doors. I think this
process runs in the 10-20K range.

I think before addressing the cabinets you should consider repainting the walls. Maybe it's just my monitor, but they seem to have a rosy glow going on that really clashes. Make the backdrop look great, then it will be easier to decide what to do with the cabinets. (I think a creamy white would look nice with the backsplash.) When you get to it, take those three uppers, remove the dividers, square-up the inset, then replace with seeded glass. Or simply go with open shelving since they aren't near the stove. Definitely remove the valance! With your high ceilings you need accentuate the vertical, not the horizontal. Maybe add some large pendant lighting. Have fun!

The valance is definitely coming down and repainting is the first thing we'll do - not only do I know like gloss, but I also just hate the tones - beige, light brown, and dark brown - but you likely can't see the dark brown part. I just don't understand why people put new, expensive countertops on worn-looking cabinets - the finish is rubbed away on some parts of the cabinets under the sink and in the island (but otherwise in good condition).

I like you lighting idea too!

I like stained wood myself. You could ask a competent refinisher to work on just those cabinets that are showing wear and keep the lighter tone. However, warm wood tones and cool grays are not a great mix - neither brings out the best in the other. Natural maple is one wood which can work OK with gray, but it helps to have a lot of a light color to pull it together, and a little bit of gray is not a problem.

It could work without the mosaic backsplash - a simpler backsplash, but if you want to keep the backsplash, painting might be the best option for the cabinets. You may lose the warmth of the kitchen though unless you can find a warm color that can work with the gray or afford a wood floor down the road.

Here is maple with gray counter, but light backsplash:

Gray is popular and people are overusing it - you have gray walls, floor, counter and backsplash - all which are making the cabinets look orange and the room - well not so cheerful:(

If the backsplash is a peel and stick one, it can be removed by heating it up with a hair dryer, but if it is a real thinset installed backsplash, then you will have to decide if you love it or not and your budget.

If this was my kitchen I would considerably lighten up the wall color to a possibly cream, put up colorful roman shades. I would trade out the gray art for something more colorful, though the piece does work with the present gray theme and because I'm not found of mosaic backsplash, I'd do something simpler that set off the pretty countertops better instead of competing with them.