Some blue jays migrate south in winter, and some do not. In fact, the same blue jays may migrate one winter and then not do so the following winter. Why they migrate when they do is a mystery. However, young blue jays may be more likely to migrate.
Adult blue jays do also migrate. Blue jays are found in forests in North America, especially when there are oak trees present. They are also common in suburban and urban environments where there are bird feeders or oak trees. Blue jays eat insects, nuts, seeds and grain. They also raid other birds' nests for eggs.