I haven't seen a better definition than the one given by George R. R. Martin in the new anthology, DOWN THESE STRANGE STREETS. I can't copy it here, since it's copyrighted material, but you can see it for yourself if you go to http://www.amazon.com/These-Strange-Streets-George-Martin/dp/0441020747/ and peek inside. His article entitled "The Bastard Stepchild" states his opinion that urban fantasy grew from hard-boiled mystery, with roots in classic horror. These are two genres, he says, that are not compatible at heart. He goes on to say that horror is set in darkness and fear, while mystery, even the hard-boiled type, is about righting wrongs and setting things right.
One can, further, find much discussion on the difference between hard-boiled and noir within crime fiction. Noir, many say, is unrelentingly dark and there are no good outcomes. This guy (http://www.defectiveyeti.com/archives/002167.html) says noir is always grim. Hard-boiled fiction is a style that has hard characters, tough guys who talk and act rough. My own opinion is that you'll find justice at the end more often in the latter.
Wikipedia (http://en.wikipedia.org/wiki/Urban_fantasy) disagrees with Martin's definition (although Martin does say that the HEROES, not the whole sub-set of urban fantasy, spring from the two opposing genres). Wiki says, alternately that it's a sub-genre of fantasy and that it's a sub-genre of contemporary fantasy. Wiki also insists on an urban setting. Although the word "urban" is part of the name, I'm not sure a city setting is required. Certainly, some of the stories in the above anthology take place in smaller places than cities, although they're all somewhat gritty.
We're calling our anthology horror, but some of our stories in ALL THINGS DARK AND DASTARDLY are urban fantasy. I don't think all of them are, but you can form your own opinion on that.
Images from Wikimedia (except ATDD cover)
Double Indemnity is a 1944 film noir. It stars Fred MacMurray, Barbara Stanwyck and Edward G. Robinson. It was directed by Wilder.
Pulp fiction cover from Wikimedia: Cover, Detective Book Magazine Volume 5, #10 (Winter 1948), Fiction House (defunct co.), pulp magazine, artist unknown
Cover of the fantasy fiction magazine Avon Fantasy Reader no. 6 (1948) featuring "The Crawling Horror" by Thorp McClusky.