Edinburgh is a city that was built to be looked at from above. The Old Town climbs a volcanic ridge. The New Town spreads across a grid below it. And scattered around the edges, a collection of hills, crags, and rooftop terraces give you completely different versions of the same skyline depending on where you stand and what time of day you get there. The geology helps: this is a city shaped by three extinct volcanoes, and the remnants of those eruptions, Castle Rock, Arthur's Seat, Calton Hill, are the reason Edinburgh's silhouette is so distinctive in the first place.
The good news is that most of the best viewpoints in Edinburgh are completely free. The even better news is that they're spread across different parts of the city, so you can chase views throughout a full day of sightseeing without retracing your steps. Sunrise from Calton Hill, mid-morning at the castle battlements, afternoon on Salisbury Crags, sunset cocktails at the 1820 rooftop. If you're here for more than a day or two, work a few of these into your itinerary and you'll see the city from every angle.