My family didn’t really do vacations. Most of my summers as a child were spent milling about in the sweltering New Delhi heat, avoiding “holiday homework,” and dreaming of being somewhere else.

So I’m pretty lucky to have spent this past holiday week in Europe, exploring two cities I’ve never been to before: Rome and Athens. Despite their different feel, they have surface similarities: Both are urban landscapes pockmarked by the grand remnants of their ancient, overlapping histories—museum-metrop…