Everyone should see ancient Rome at least once.
Italy's capital delivers a marvelous (and relatively inexpensive!) European holiday that does everything at least as well as every other city on the continent, from culinary excellence to classic art. Rome's shopping and sightseeing are also quite literally world class.
While you're exploring the city, inevitably you cross the Tiber river and enter the east side of town where you're met with the remains of one of the world's greatest civilizations. The Roman Empire spanned 13 centuries, and the rubble - some of it patched up and rehabilitated - is all that physically remains.