Since it came to my city, Natural Grocers has become a new favorite shopping destination for dairy-free. They have very high standards for the products they carry (all natural and banishing a list of questionable ingredients). Their produce department is 100% organic, and they carry tons of hard to find dairy-free and gluten-free conveniences, most at notably lower prices than Whole Foods. And they have great sales.
Dairy-free staples that I buy at Natural Grocers include in-season organic produce, unsweetened So Delicious coconut yogurt (no one else carries the unsweetened!), dark chocolate (there is almost always something good on sale!), Yogi tea, Muir Glen canned tomatoes (especially those fire-roasted ones), and dairy-free milk beverage. Their frozen food section and supplements sections are also quite large, and they carry many vegan alternatives for cheeses and meats, but what Natural Grocers does lack is “fresh” foods, beyond the produce department – there are no meat and seafood departments, deli counters, or other items prepared on order.
Natural Grocers has locations dotted across the U.S. (they are a Vitamin Cottage chain), and are rapidly expanding. See their website for current and upcoming store addresses.