My thought is that if you want to keep on with the defining the character and moment you need more interesting/telling details to carry it off. Otherwise, get the storyline started after one or two of the more interesting details.

Your verb tenses are a little off. Here's the rest of the nitpicky:

I don’t know how long I've sat "I sat" would work better, I think, or "I've been sitting here." Presumably he's still there, right? there, perched like a gargoyle on the thin rail of the hotel balcony. The unfamiliar city has become sleepier as I watch Hrm... present tense is tricky. I think "becomes sleepier as I watch" or "has become sleepier as I've watched". Laughter from couples returning from adventure and stumbling in embrace to the hiss of the doors five floors below is less frequent it seems Less frequent than what? I thought it's an unfamiliar city. Also, this image is a little cliche.. Cold and impersonal, relays click and the lights dim on the nearby office buildings—empty parking lots became dark voids without ceremony. I watch as the world goes on late shift.
I feared heights once, but I know now such is a trivial thing; a personal phobia I didn't think this really added anything. What else but a personal phobia would a fear of heights be?.
There are far greater things to fear out there. Loneliness seemed my demon of choice tonight. Even that is inconsequential as I look beyond.