The Sun does not go round the Earth each day. Earth spins, once a day, around an axis through the North and South Poles. At any moment the half of Earth facing the Sun has day and the other half has night.

The line between them is the terminator. As Earth turns, your town is carried across it: into daylight at sunrise, out of it at sunset. From the ground it looks as if the Sun moves across the sky from east to west.