|MadSci Network: Astronomy|
Since we are in the milky way, we cannot see it as a whole at one time.
[Of course, different parts of it can rise and set at different times, but in general, some portion of the Milky Way can always be seen. Moreover, since all of the stars we see are part of the Milky Way, one could say that the Milky Way is always up! Moderator.]
Now, if we were on a planet in a different galaxy, we might see the Milky Way moving in the sky, but that would be from our own planetary motion. However, the sun rising and setting is also relative, something that we perceive because of motion of the Earth.
Now, if you want to get into more detail, let's say that we weren't on a planet in another galaxy, but we were in intergalactic space, far away from the Milky Way (intergalactic space is the space between galaxies, there's not much there besides a few atoms per square inch). If we were hovering there, we would still see the Milky Way moving. For one thing, even if you're in space, you still might not be stationary.
Not only that, but the Milky way itself spins, and so even then you would see it moving, but not rising and setting.
All of this takes time. If you were viewing from the surface of a planet, it would take a whole year for you to see the Milky Way's movement in total. And that's nothing! If you were looking for the Milky Way's spinning, you would have to wait 200,000,000 years to see it make one rotation.
Try the links in the MadSci Library for more information on Astronomy.