It's worth searching for "vegan" on CouchSurfing or Warm Showers. I've had much better responses from vegans when traveling than from non-vegans. I suspect that vegans in more remote places don't know that many other vegans nearby, which means you'll be welcomed with enthusiasm and a great meal. That's a double win because those places are where you'd otherwise have fewer food options.

Most supermarkets in urban and suburban areas at least have things like soymilk and clif bars, but even if they don't my staple meal is a bowl of oatmeal. I'm allergic to most nuts so my basic lunch is two hummus and avocado sandwiches (though avocado is expensive in some areas). My biggest mistake has been limiting my emergency food to clif bars; after a few too many of those things you won't want to see another one for months!

Check sites like happycow.net to fins vegan-friendly supermarkets and restaurants.