B.M. Gray Wisp would work well....it is gray (cool against the warm cabinets) with strong green undertones (again cool). Ask your S W dealer to match the B.M. formula. If Gray Wisp is too dark, find the S W equivalent of B.M. Paperwhite

You can also save a bit of money, by painting the backsplash. I think, everything white, is a bit too much. You can get a sample of the blue you like, and put it on poster paper and tape that over the lower cabinet, to see how you like it. White on the top would be fine. If you are going to do them yourselfs, preparation is very important. Clean them, with a very good cleaner. Sand them, if any nicks, or dents, or holes, then fill those, and sand again. Wipe them down really well, and use a top quality sealing bonding type primer on the cabinets. Follow the directions on the can for dry time, paint coating time, and if that primer needs a very light sanding. Then wipe them down again, and start painting. Some can be done with a small foam (white) roller that says, for cabinets on it. Also, make sure the paint you are putting on, is an actual cabinet paint. It will take 2 to three coats. Follow the directions on the can for drying time, before recoating. Let sit a couple of days, before trying to hang the cabinets, and like above, do not close them, for 30 days. Primer the backsplash with sealing bonding primer. Use decent quality satin or semi gloss paint to paint them. Make sure they are squeaky clean, before doing anything to them. Trim, could be satin or semi gloss white. A nice light color on the walls and you will have a fresh clean kitchen. Do not rush any of these steps. Take your time, and do it right. It is time consuming to paint cabinets, and do a decent job. There are NO shortcuts.

I would paint all the walls in Greek Villa first and then decide if you need an accent wall. Few spaces really benefit from an accent wall ...

With that rug and flooring - I'd definitely splurge on a dark blue. Arguably it's just as neutral as a color of white and will be plenty flexible for future design choices. Here's a range of some of the best dark blues.