1. Arthur's Seat
Arthur's Seat is an ancient extinct volcano rising 250.5 metres (822 ft) above Edinburgh, forming the highest point of Holyrood Park. Robert Louis Stevenson called it "a hill for magnitude, a mountain in virtue of its bold design." It sits about a mile east of Edinburgh Castle and is geologically around 340 million years old — the remnant of a volcano active during the Carboniferous period. The name has nothing to do with the legendary king; most historians trace it to a corruption of Gaelic meaning roughly "Height of Archers."
The summit gives a full 360-degree panorama: the Firth of Forth to the north, the Pentland Hills to the south, and the Old Town skyline directly west. Several routes lead to the top, from a gentle grassy slope from Dunsapie Loch on the east side to the more demanding scramble up via Salisbury Crags. The climb from the Palace of Holyroodhouse takes about 45 minutes at a moderate pace, passing St Margaret's Loch and the ruined St Anthony's Chapel on the way.
This is genuinely one of the best places to visit in Edinburgh, partly because it's free and partly because it's the real thing — a proper hill walk with weather, boggy ground, and views that put the whole city in context.