Even though it might not look like much when it's so far away, the Moon is pretty huge. In fact, if it was a little closer—as close as the ISS for example—it would monopolize the entire sky.
Yetipc1, apparently a serious astronomy nerd, took the liberty of figuring out what it would look like if ol' Luna was a mere 270 miles out, instead of the 238,855 miles it actually is. Suffice it to say it looks a bit...different. Destiny, anyone?
Yetipc1 explains some of the trickier details in the video's description:
Normally the Moon orbits much slower than the earth rotates so it rises in the east and sets in the west, however at 420km it orbits much faster, faster than the earth rotates underneath, therefore it will rise in the west and set in the east.
...The Moon would orbit very fast, somewhere between 130 mins and 90 mins. ...The time in the video is sped up. The moon would transverse the sky slower. Like 10 mins (rough guess)