big life; small space

As someone who's currently studying abroad in Rome, yes, Trastevere is enormously different than what you describe. My writing teacher described it as "the Italian neighborhood of Rome"; shockingly expensive apartments, hole-in-the-wall coffee bars with amazing cioccolata calda, fantastic pasticcerie and gelaterie, and at night the tiny web of alleys around the Piazza di Santa Maria are packed with young people and old people and foreigners and hipsters. There's a shop where you can buy absinthe and alcohol in chocolate shotglasses and books, and a bar with a scrawny tattooed Italian prettyboy dressed as Axel Rose for a bouncer. It's honestly one of my favorite, liveliest, safest places to be out until four in the morning in Rome. Weird to imagine it otherwise.