Nuclear fallout is defined as the residual radioactive ash that falls after some kind of nuclear disaster has happened. With that in mind, the spread of nuclear fallout can vary from episode to episode.
Chernobyl, for example, had a fallout radius of 30 kilometers, or 19 miles. In fact, it is still radioactive in most, if not all, of that original fallout radius. The fallout from the bomb dropped on Hiroshima had a fallout radius of about 1.6 kilometers, or 0.994 miles.
The previous answer gives a ton of details about how fast nuclear devices can go, so for a better idea of a universal value, see that answer as I cannot go into detail about that here.