Jay Gatsby is, indeed, a hyperbolic character in Fitzgerald's The Great Gatsby, at least as presented to the reader by Nick Carraway. In Chapter One, for instance he is described by Nick, who "wanted no more riotous excursions with privileged glimpses into the human heart"--itself a hyperbolic declaration:
If personality is an unbroken series of successful gestures, then there was something gorgeous about him, some heightened sensitivity to the promises of life, as if he were related to one of those intricate machines that register earthquakes ten thousand miles away,
Also in Chapter One, Nick describes the two areas twenty miles from New York city as "enormous eggs,"
identical in contour and separated only by a courtesy bay,[that] jut out into the most domesticated body of salt water in the Western Hemisphere, the great wet barnyard of Long Island Sound.
Tom Buchanan is also described with Nick's penchant for exaggeration in this first chapter:
I had no sight into Daisy's heart but I felt that Tom would drift on forever seeking a little wistfully for the dramatic turbulence of some irrecoverable football game.
Certainly, in Chapter Four, the mythological description of Gatsby's car by Nick is another example of hyperbole:
It was a richcream color, bright with nickel, swollen here and there in its monstrous length with triumphant hatboxes and supper-boxes and tool-boes, and terraced with a labyrinth of windshields that mirrored a dozen suns. Sitting down behind many layer of glass in a sort of gree leather conservatory we started to town....
With fenders spread like wings we scattered light through half Astoria....
Additionally, in this Chapter Four, Nick describes their ride in similar terms:
Over the great bridge, with the sunlight through the girders making a constant flicker upon the moving cars, with the city rising up across the river in white heaps and sugar lumps all built with a wish out of non-olfactory money.
It seems appropriate to his themes that Fitzgerald employ this exaggerated prose in depicting an age characterized by excess and frivolous behavior. Indeed, his prose is an example of art imitating life in the Jazz Age, a time when men chased an illusionary dream.
Hyperbole is exaggeration used for effect, and frankly the entire novel is rather hyperbolic. I mean, you have these hugely rich characters living on this grand scale--everything about them is rather big and melodramatic. Juxtaposed with them is Nick's little shanty of a cottage and the ash heaps with Wilson's Garage. Few real things are truly that dismal, just as few real things are so sparkling and grand. I presume, though, you're more interested in some actual written hyperbole, so that's what I shall offer.
Consider the descriptions of George Wilson:
"There was not enough of him for his wife" (chapter 8).
"Wilson...went toward the little office, mingling immediately with the cement color of the white walls" (chapter 2).
"'He's so dumb he doesn't know he's alive,'" says Myrtle of George in chapter 2.
These descriptions are all exaggerations, of course, and the valley of ashes itself is rather a hyperbole.
The descriptions of Gatsby's party-goers are always rather exaggerated:
"They conducted themselves according to the rules of behavior associated with amusement parks" (chapter 3).
Again, though, part of that is the elaborate nature of the parties and the party-goers.
Nick, the narrator, describes Gatsby in what may be considered exaggerated terms, as well:
"It was one of those rare smiles with a quality of eternal reassurance in it, that you may come across four or five times in life" (chapter 3).
"Gatsby, who represented everything for which I have an unaffected scorn" (chapter 1).
"It was an extraordinary gift for hope, a romantic readiness such as I have never found in any other person and which it is not likely I shall ever find again" (chapter 1).
Again, though, Gatsby is this larger-than-life character--especially from the perspective of time from which Nick writes. Note, though, the use of never, any, ever, everything, eternal--words which should not generally be used in description for the very reason that it is exaggeration.
Hope that gets you thinking about others you might have read.