Can you help me identify an insect that I see in the height of summer? It looks like a black and off-white moth or butterfly in flight, but when it lands, it looks like a dull beige- or gray-colored cricket.
What you describe sounds like a road duster, also known as Carolina grasshopper (Dissosteira carolina). According to Merrill Peterson’s Pacific Northwest Insects, it is often found on dusty or dirt roads and paths, sidewalks, and sandy beaches. It is not easily noticed until it flies, flashing its patterned hindwings. The hindwing pattern is unique to this species, though it somewhat resembles the Mourning Cloak butterfly. They are mostly active in the daytime, and seem to be generalists about food, eating grasses and forbs (herbaceous flowering plants) from what is available in their habitat.
This page from University of Wyoming has additional information about its food and migratory habits. A page on insects of eastern Washington mentions that birds, bats, praying mantis, and spiders eat Carolina grasshoppers.