Yes Vatican City is on a hill in Rome. No Vatican City is not on one of the seven hills of the ancient city of Rome.

One of the important aspects of Biblical Interpreteation is to know a bit of history. When the book of the Apocolypse was written (as tradition tells us) by St. John the Apostle, the ancient city of Rome was on seven hills, the Vatican Hill is outside of the boundries of the ancient or original seven hills of Rome.