Princes Street Gardens is a valley garden in a drained loch — the Nor Loch was emptied two centuries ago to build the New Town, and what's left is a long green trough with the castle rock standing over it like a held breath. There's no better place to understand Edinburgh's two halves than down here between them.
Under three kilometres, gentle, and best on an afternoon. Start beneath the Scott Monument, the largest thing ever built for a novelist; climb its 287 steps or simply stand under the soot-black Gothic spire. Drop into the gardens past the Floral Clock — the oldest in the world — to the Ross Fountain, all mermaids and walruses, freshly restored and posing under the castle.
Walk the lower path right beneath the crag, then up the Mound, the ridge of New Town spoil that carries the two great temples of the National Galleries. Go in; it's free, and the Scottish rooms reward it. Leave by St Cuthbert's, its watchtower built against grave-robbers, and walk on to Haymarket for the train or tram.