Best Non-dairy Milk Alternatives. My Picks for the Top Dairy-free milk Substitutes. The good news is that most stores carry many varieties of non-dairy milk alternatives, including soy milks, rice milks and almond milks, both in non-refrigerated boxed products as well as refrigerated varieties. The bad news for many new to the dairy-free diet, however, is that most stores carry many varieties of non-dairy milk substitutes!