The Steffen app allows you to see in real time the position of the sun or moon at any point in world. By default it uses your current location to cast a shadow in the same direction as the sun or moon and displays a little compass at the bottom of the screen.
The app tells you how long until sunrise or sunset depending on if it is currently day or night and updates with nice backgrounds that are suitable for the time of day.
You can also search for anywhere in the world in the settings screen and see where the sun or moon would be as if you were standing there!