Great Hotel for Price & Location
Yes, the rooms are small (this is New York), it's not the quietest place (it's right on Canal, so, yeah, not a quiet street), but the rooms are clean and reasonably priced. Hotel Azure is situated in prime New York City Territory - the edges of Chinatown, Little Italy, SoHo, and TriBeCa. In fact, it is pretty much on the edge of the once notorious Five Points (i.e. where Gangs of New York was set).
In addition to being able to wander around that interesting, diverse location, there is a Subway station right at there on Canal that can take you to Uptown, Downtown, Central Park, Times Square, Union Square, Williamsburg, etc.
There is no bar or restaurant in the hotel (or room service), but, again, considering the location, there are plenty of great options just around the corner.
As for the noise, I slept fine, it never bothered me.
Finally, the room size shouldn't matter - if you're in New York City why are you spending more time than necessary in your hotel room?