Asking about literary sites in Rome sounds to me like asking about the wet spots in the Atlantic Ocean, but here are a couple off the top of my head:
• Augustine's mystical vision described in his Confessions is set in Ostia Antica, where he was sharing an apartment with his mom. Monica deserves to be sainted for putting up with his shenanigans, and so she was, and is today the patron saint of mothers with disappointing children. Originally buried in Ostia, her remains were later moved to Rome and placed in the Basilica di Sant'Agostino in Campo Marzio.
• Haruki Murakami wrote most of his breakthrough novel Norwegian Wood (1987) while living in Rome. He and his wife were consciously following in the footsteps of Zelda and Scott Fitzgerald by bumming around the Mediterranean in the mid '80s.
• Giles of Viterbo, the Augustinian Bishop who is unfairly considered a bogeyman among Lutherans because he was the official who told Martin Luther to straighten up and button his lip when Luther made his pilgrimage to Rome to whine about being ordered to get along with congregations he didn't like back in Erfurt (because the pope was out of town when Luther was visiting) was a renowned scholar of Kabbalah and the Hebrew Scriptures, and he worked with manuscripts that are still available in a branch of the public library in Rome, the Biblioteca Angelica which is considered the oldest public library in Europe along with the Biblioteca Ambrosiana in Milan.
https://en.wikipedia.org/wiki/Biblioteca_Angelica
https://bibliotecaangelica.cultura.gov.it