Cool grays and warm toned woods do not look great together - neither does anything for the other and often it looks a bit dark and drab. Barely there gray can work. Warm toned woods look best with creams, creamy beige, blues and greens. The blues and greens can have gray undertones. Creamy and light colors brighten the space and let the wood look at its best.

Consider changing your flooring first. If you do the kitchen, it will feel like wood overload at first - but give it a month. I know I felt that way at first but now I love my wood floors. Consider a lighter stain to a natural look. I am seeing much more of that then the darker stained floors now. This may be due to the darker floors showing more dust and scratches than the more natural tone. The dark floors and gray walls look is still popular, but waning in some areas - so don't go with that look unless you absolutely love it. To make that look work, you would probably need to paint or replace the cabinets - it just doesn't work quite the way you will want with the warm wood tones. It may be get very expensive to change the whole house to cool tones - only to have that trend out just as you get done.

Here are two pics from the 2016 season of This Old House. Notice the warm woods and the island is actually oak. This is a classic, warm look rather than trendy look. The walls do have a gray sense to them, but are not "prison wall gray" and keep the space light.

I agree that your kitchen is not bad at all. I am not overly fond of the flooring, but you have said that will be changing - and even the flooring is not that bad.

I have older oak cabinets - I do have a much lighter countertop but yours is very nice. My kitchen is in my "my pics" idea book - it is a more cottage style, but the sink, countertops and backsplash are versatile to many styles.