Try Magical Realism. It's like Urban Fantasy with the fantasy toned down.
I'm not sure it's really something different. Urban Fantasy tells you two things are present: and urban (presumably modern urban) setting and fantasy elements. That certain tropes have crept in as being dominant doesn't make those dominant elements *more* urban fantasy than books without those tropes. Too many genres classifications is really *more* confusing than just a few broad categories, IMO.
Richard Kadrey has written a couple of comic urban fantasy books that are pretty different than what you're describing. I am also very sick of that kind of protagonist (whether male or female).
>The use of existing monsters or mythologies but in a city setting
That's literally the definition of urban fantasy?
I don't know what you'd call the genre, but I'd like to recommend Mieville - particularly *Perdido Street Station*, *The Scar*, & *Iron Council*, but really anything by him. These tend to be classified as "Weird Fiction" and are a little more steampunk-y than regular urban fantasy, but they are definitely "fantastical" and mostly urban :)
I would really suggest the New Weird short story anthology, it has several great and tremendously original urban fantasy stories, without aforementioned cliches.
Though If I were to pick novels, Perdido Street Station by China Mieville has fairly interesting setting,
and while it uses a bit of pre-existing mythology, it is so far removed from any resemblance to it, as to be indistinguishable, Vellum by Hal Duncan is a tremendous read.
That's still Urban Fantasy, just without devolving into a bad parody of hardboiled/noir conventions.
Have a read of Fritz Leibers Conjure Wife and Our Lady of Darkness.
The tough-as-nails female protagonist who falls in love with a supernatural character/creature.
This annoys the hell out of me, and these usually turn into a really really shitty romance novel which is a mix of twilight and 50 shades.
I think Urban Fantasy fits the genre well..Try the Paul Cornell books for Urban Fantasy without any of the tropes above, but Id recommend you read them in order or you wont understand some of it. Series starts with London Falling, there are only three books so far, and Im really hoping for more! Dark and gritty.
[Contemporary fantasy](https://en.wikipedia.org/wiki/Contemporary_fantasy), of which urban fantasy is a subset.
Some books I have enjoyed which fall in this category are:
Manly Wade Wellman - The John the Balladeer Stories
* protagonist is a traveling balladeer, a civil and respectful person, and a pacifist.
* setting is rural Appalachia.somewhen alter the Korean War.
Charles de Lint - The Newford books
* Different protagonists, often "common people" who aren't especially strong (whether normal or supernatural).
* Uses mostly native American mythology but in a very organic way.
Dennis Danvers - The Donut Man, Wilderness or Bad Angels.
* Protagonists are either middle-aged men (a professor and the owner of a donut shop) or a supernatural (fallen angel who isn't very badass)
* Urban settings mostly but they focus on a very small group of characters with no "wider magical world".
Chuck Wendig - Miriam Black stories.
* The protagonist is a woman with a psychic power. Not especially strong.
* No mythological monsters.
* Books are "on the road"and on the gritty side of American life.
Little, Big by John Crowley.
I'd recommend [Pact](https://pactwebserial.wordpress.com), since it fits all of your criteria.
It's got some pacing problems (the author himself called it a "learning experiment"), but the way magic works in Pact is excellent and while Blake isn't Wildbow's best protagonist he's a good contrast to the rest of the major players, being humble, empathetic, and meek.
But seriously, the magic and setting is *cash*, and once the cast is fleshed out the banter is A1 as well.
*Good* urban fantasy.
Okay, I know that's mean. To give an example of avoiding this, Robin Hobb's *Wizard of the Pigeons* hits zero of OP's bullet points but nobody remembers it.
Charles de Lint might fit? I read "The Painted Boy" last year and while it does make use of a "Dragon" it's in a fairly different way. The protagonist is a teenage boy learning his powers. Wikipedia refers to his subgenres as "urban fantasy, contemporary magical realism, and mythic fiction"
The Bartimaeus Trilogy has "The use of existing monsters or mythologies but in a city setting," but it doesn't use the other two big tropes associated with urban fantasy. There is a fictional play in it called "The Swans of Araby" that is basically a parody of stuff like Twilight. Shame that it doesn't get more love IMO.
Hi! Did you know that Richard Kadrey [did an AMA here?](https://www.reddit.com/r/books/comments/3irqjh/hello_this_is_richard_kadrey_im_the_author_of_the/?ref=search_posts) you might want to take a look :) [Here'sa full list of our upcoming AMAs](https://www.reddit.com/r/books/wiki/amafullschedule)
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