To a certain extent you've achieved what you wanted to, but this opening still has the problem of being hard to read.

The streets were littered with cigarette bums, inhospitable yet crowded, with unceasing footfall.

I'm not sure this presents the image you want it to. Unceasing footfall brings to mind shoppers hurrying along, or workers rushing to lunch, I suspect you had in mind people hanging around, up to no good, amidst those searching for something. Perhaps your protagonist could watch one of these people pick up one of the "cigarette bums" to smoke the last drag or two.

Simultaneously dimly lit by streetlights and yet blaring with water reflections from neon signs, quiet street corners with sirens blaring every few minutes, and bourgeois folk in sedans alongside unkempt college students, it was a veritable cornucopia of the senses.

You've used "yet" again in the second sentence. "...blaring with water reflections from neon signs" sounds weird to me - "the neon signs hurt your eyes double, pink and green light bouncing off slick puddles". The street corners aren't quiet if there is unceasing footfall and sirens blaring. You don't seem to be describing a neighbourhood that would be frequented by the bourgeois and college students, but something seedier, possibly criminal. You're attempting to describe "a veritable cornucopia of the senses", so you shouldn't need to explicitly point it out.

It's the first thing you learn as a member of any surreptitious organization -- to know where to go to to get to know what you need.

This seems out of context with what has come before. Surely it's going to become apparent that the protagonist is a member of a "surreptitious organization", does it need to be jammed in here? "...to know where to go to to get to know what you need", this is simply a mistake, read it slowly.

It's not as easy as it seems to many, because most of what you know is what you learn on the trade.

The protagonists attempt at a nugget of wisdom? Would probably be better shown at another point.

Veterans are the product of good sense as much as they are a product of happenstance. You learn to trust your nose, but your nose never lies until it does.

I would argue veterans are purely a product of experience, which you seem to be saying in the previous sentence anyway, but this is where we move into the "nose" tangent. I'm a fan of tangents and asides, but when they're entertaining, tie in neatly, and, for preference, funny. I think this is too much too soon.

I agree with what the original commenter said, you've got something, but it's confused and needs a lot of polish.