ANN ARBOR, Mich. National Doughnut Day is June 5. While the doughnut as we know it today came to the United States through New York, Ann Arbor has a few favorite doughnut destinations of its own. Celebrate circles of doughy goodness by checking out these Ann Arbor area businesses this weekend. You may know Washtenaw Dairy for its ice cream but the decades-old Ann Arbor dairy also does doughnuts. Avalon Cafe and Kitchen Ann Arbor and The Songbird Cafe also have pastries and desserts of different types.