“Where is the Galaxy taking us?”

Towards the andromeda galaxy which is over twice the size of the Milky Way. We are hurtling towards each other at about a quarter millions miles per hour.

For thousands of years after you die, that little fuzzy spot near Cassiopeia will slowly get larger and larger in the sky, and in about a four billion years, long after the Earth's oceans have dried up and the sun is a giant, reddish monster hovering in the sky, and our magnetic field will have long since died out, our atmosphere will have been mostly stripped away and the weather will feel like being on the highest mountains in an oven, the night sky will be covered with a dazzling display of the Andromeda galaxy overhead, spiral arms visible with the naked eye stretching from horizon to horizon.

We will merge, in a series of passes through each other, with almost no stars actually colliding most likely, although a good number will be ejected into the emptiness of intergalactic space, and will finally settle into a new shape, and may trigger a new phase of star formation as new clouds of gas and dust collide and collapse in the new super-galaxy.