I saw a rocket (not a shuttle) launch at night (2 am) once, and didn't have to fight any crowds. I simply stood out in the parking lot of my hotel in Melbourne, FL (south of Cocoa by, what, about 20 miles or so?). Even from that distance, it was absolutely awe-inspiring. And yes, it really does light up the sky.

I also once saw a shuttle launch, again without fighting crowds. This time I was on Kiawah Island, just south of Charleston, SC! It was just at sunset, so the flame was visible against the darkening sky and the smoke plume was well-lit by the setting sun. In mid-day it might not have been visible, and at night it might have looked like a bottle rocket. But as it was, it was spectacular.