I wouldn't bother painting the vanity as painting won't change the style of it, and natural wood is popular again. Also, painting cabinets is either an expensive or time consuming (DIY) project when done correctly. Look into products to revive the wood if it's a little banged up. Or if you must paint it, I would be looking at a creamy color. Pick out any of the colors in the granite. In any case, changing the other elements you mentioned will give you good results for the effort.

The wood you have now is actually more contemporary and current than the painted looks AI is giving you. Are they in good enough condition to leave unpainted? I see a raw area. Could you use a stain pen on that?

I'd leave as it. Your vanity itself doesn't need to be the wow moment in the room. Your fixtures should do that instead. Get chrome hardware, chrome faucets. Contemporary chrome mirrors with some interest to them. Great over the counter lighting. Paint all of the walls a soft white. I don't know if these are your style but they would add interest to the room.

The cabinets are in good condition besides the raw area we can fix. I don't love the chrome. Would black not look good?

I would paint this room an off white or cream color (no yellow undertones) They floor will help you decide which white. I would also add greenery/plants to this bathroom. White shower curtain

What are your thoughts on fixtures and cabinet color?

I agree fixtures (lighting/hardware) are dated. I would stick to chrome as it is timeless choice for bathrooms. No black. The mirrors are fine. I would not paint the cabinets unless they are professionally done. Instead get a wood restoration product to rejuvenate the cabinets first.