I cannot recommend this practice highly enough, even though I've only done it twice. The second book-and-city combination was Joanna Scott's Arrogance in Vienna. The first was George Eliot's Middlemarch in Rome.
Here is the passage that lingers in my memory. Dorothea, the novel's heroine, has just arrived in Rome with her much older husband, Mr. Casaubon, and is experiencing an unaccountable sense of desolation:
She had been led through the best galleries, had been taken to the chief points of view, had been shown the grandest ruins and the most glorious churches, and she had ended by oftenest choosing to drive out to the Campagna where she could feel alone with the earth and sky, away from the oppressive masquerade of ages, in which her own life seemed to become a masque with enigmatical costumes.
....The weight of unintelligible Rome might lie easily on bright nymphs to whom it formed a background for the brilliant picnic of Anglo-foreign society; but Dorothea had no such defence against deep impressions. Ruins and basilicas, palaces and colossi, set in the midst of a sordid present, where all that was living and warm-blooded seemed sunk in the deep degeneracy of a superstition divorced from reverence; the dimmer but yet eager Titanic life gazing and struggling on walls and ceilings; the long vistas of white forms whose marble eyes seemed to hold the monotonous light of an alien world: all this vast wreck of ambitious ideals, sensuous and spiritual, mixed confusedly with the signs of breathing forgetfulness and degradation, at first jarred her as with an electric shock, and then urged themselves on her with that ache belonging to a glut of confused ideas which check the flow of emotion. Forms both pale and glowing took possession of her young sense, and fixed themselves in her memory even when she was not thinking of them, preparing strange associations which remained through her after-years.
As it happened, that same sensation of bewilderment, of being unequal to the glory and squalor of Rome, I experienced when, at twenty, I sat down in the Piazza Navona with my copy of Middlemarch. The novel helped me to understand myelf and to place myself in the larger contexts of history and evolving human experience. And if fiction can't do that, what's the use of it?