Calton Hill is Edinburgh's easiest classic view: a five-to-ten-minute climb up a stepped path from Waterloo Place gets you a monument-studded skyline that most cities would build a funicular for. At 103 metres it's less than half the height of Arthur's Seat, there's no scrambling involved, and you're back down in time for dinner. If you've only got twenty minutes free in the city, this is where I'd send you.
It sits right at the eastern end of Princes Street, a couple of minutes from Waterloo Place and the top of Leith Walk, and it belongs alongside the rest of the city's big free sights in our things to do in Edinburgh hub. It's also the headline entry in the best views in Edinburgh, which covers eleven different viewpoints in a paragraph each. This page is the deep-dive on Calton Hill specifically: every monument on it, what's free and what isn't, and honest sunset timing that actually accounts for the season.
Five things share the hill: the unfinished National Monument, the paid Nelson Monument with its daily time ball, the Dugald Stewart Monument (the one in every skyline photo), the old City Observatory, now home to the Collective gallery, and the Political Martyrs' Monument, which is actually a few minutes' walk away in a different spot entirely. Here's what each one costs, when it's open, and which you can skip if you're pressed for time.