The closest to OKW is about 2 miles - Goodings down at the Crossroads - but it is fairly expensive and can be a tough trip when temps are high - especially the return trip with groceries (ask me how I know).
From AKV there is a convenience store about 2 miles away out on 192, but it would be more like 5 miles to a regular grocery (Publix - also on 192). You can see Kidani village from the Publix area and it's probable 1/2 as the crow flies, but there is no easy way to get there - unless you have a crow.
You might want to consider a grocery delivery service like Garden Grocer or WeGoShop and enjoy running without the need to carry groceries at the same time.