Calton HillLow hill at the east end of Princes Street, with monuments at the top and a wide view over the city. A short climb on steps and paths.
Free
Holyrood Park and Arthur's SeatOpen hill park at the end of the Royal Mile, with the climb to Arthur's Seat and the lower Salisbury Crags walk. Exposed and often windy, with proper shoes needed.
Free
Inverleith ParkLarge park opposite the botanic garden, with a pond, playground and a clear view back to the castle.
Princes Street GardensGardens in the valley below the castle, with lawns, a playground at the west end and the Ross Bandstand. The main green space in the centre.
Royal Botanic Garden EdinburghTwenty eight hectares of gardens north of the centre, free to enter, with lawns and a rock garden. The glasshouses are ticketed separately.