Is it normal that I constantly crave to walk through a dark, empty city at night, to find some place with a good view to sit and think? I've been doing this for a few weeks, and it's become a habit. Usually I'll go walking at three in the morning for a good few hours. Please answer, it's seriously messing with my sleeping habits.

I love how the city has an entirely different life at night. People only think of cities as daylit commercial centres. They never realise that the city they think they know is shared by those who inhabit it at night. It's an entirely different place then, when the darkness falls.
I've always felt slightly more at home with the night shift, the whole twisted, mad carnival of it all.
I guess, for you, you could go with the Spanish model of sleeping twice a day rather than once (and which is generally thought to be better, anyway). Or you could just swing your day around by four hours so rather than go to bed at 11pm and wake at 7am, you go to bed at 7pm and wake up at 3am, and start your day with some night-thinking. For me personally, I'd rather end the day with the night, than start it though.
I sometimes have a short nap in the afternoon if I have free time so I can stay up late.