Kitchen off family room

Granite in natural light.

I'm confused. Do you want a white to coordinate with the existing tile or are you changing the tile and thus just wanting a good "kitchen white?" Do you like high contrast, cooler whites or lower contrast warmer whites?

Either way, there are 500000 shades of white. Most of the discussion on here is with the Benjamin Moore colors. BM Simply White is very bright but not too bright. Chantilly Lace is also very bright, more like a true white white. White Dove is nice white with slight gray undertones. Cloud White is nice, bright but with some warmer undertones. Linen White and Mayonaise are Mascarpone are all more creamy... But lighting affects absolutely everything so you will probably have to paint up some sample boards and live with them for a while to see how they read in your home. For example, I was sure I wanted White Dove. My friend has the same color and it looks gorgeous in her kitchen... but it looked more dreary in my kitchen with little light.

Do a google search "White Cabinets Gardenweb" and you will find a bazillion threads about all the different whites.

Thanks for the tips. At this point, I don't think I have much of a choice and will have to change the tile. I guess I'll have to match the white to the granite and hardwood.

Your cabinets (what I can see of them) are beautiful. But if you really want white, then I can only echo what lesmobo said.
I went to several paint sources and grabbed umpteen white paint chips. At home, I sat down in the kitchen and also outdoors in bright but indirect sun and sorted them into piles of undertones I liked and didn't like. It really was easier than it sounds. Then I taped up about a dozen "finalists" on the walls to see how they looked at different times of day, under the lighting that I would be using (LED).

I was looking for a warm gray rather than full-on white and settled on Behr "Campfire Ash". However, my cabinetmaker couldn't match that and went with my 2nd choice, Martha Stewart "Gull" which is less gray and warmer, sort of what we used to call bone.