Shooting the night sky is one of my favorite things to do. A clear night under the stars is something amazing - when you look up and stare at the stars, you realize just how small we really are: we are a speck on a larger speck in a much larger arena that we can't even fathom the scale of.
One of my favorite places to shoot night photos is in Colorado. There are so many parts of Colorado that are dark at night; I have had several nights where I just look up in the sky and I can clearly see the Milky Way. My first experiences shooting the night sky were when I was living in Colorado. I purchased a Rokinon 14mm lens as reviews all said it was fantastic for astro photography and it was fantastic value. It took some time to get it all figured out (camera settings, lens adjustment, composition, etc), but it became addictive.
Over the years I have gone from shooting night scenes in the mountains to shooting them along the Oregon coast, the Alps, the Cinque Terre in Italy and even the northern lights in Iceland. Each place offers it's own unique set of characteristics and challenges.
The Oregon coast, for starters. Shooting night scenes in the mountains doesn't pose many dangers in many regards. You find your location, you setup your gear and then you hangout and enjoy it. The coast, on the other hand, you are by the ocean in the dark and if you have ever been to the Oregon coast, it's not a calm place. You keep your eye on the water as best you can, but all you hear around you is waves crashing on the shore. I won't lie, it's a bit terrifying. I do my homework and at the least know the tide prior to sending off on an adventure, but that doesn't much change the lack of visibility. Basically, be safe if you go and shoot ocean scenes at night.
The Alps. First off, if you haven't gathered, the Alps are my favorite place I have been. The size, the drastic landscape, the rugged peaks; everything about them is amazing. Now, I admittedly, I haven't shot much of the Alps at night, but the places I have resulted in stunning photos. I was fortunate to get a few clear nights over Chamonix to capture the Milky Way over Mont Blanc. I also was lucky to get a few clear nights in Switzerland as well while in Lauterbrunnen (which if you have been to Switzerland, this is a rare occurrence as it's cloudy there quite often!).
From the Alps we went to the Cinque Terre on this recent trip. Unfortunately the moon and the lights of the towns were too bright to capture the Milky Way, but I did have clear skies which resulted in some beautiful night scenes near the town of Moneglia.
The northern lights were something new to me, not necessarily in seeing (I had seen them once before growing up in Wisconsin), but definitely in photographing. What I typically use for my settings to shoot night scenes was completely unnecessary as the northern lights are much brighter than a starry sky. The technical aspect aside, WOW...WOW is all I can say! The sky quite literally dances at night; colors shooting across the sky, waving back and forth, the movements and colors are unreal!
Regardless of where you are, the night sky is incredible. Get outside, look up and enjoy it! A few helpful sites to make your night viewing a bit more enjoyable:
http://darksitefinder.com/map/ - See where the nearest dark area is in location to you.
http://www.aurora-service.org/ - KP index and map for North America. Very helpful and necessary for knowing when you might be able to see the northern lights.
http://www.aurora-service.eu/ - Same site, but for Europe.
Also check your local forecast to see what the weather is like; overcast skies make for a rather uneventful evening.