One thing I would recommend doing in Edinburgh if you can, is to go up the Calton hill. From the Barmoral Hotel at the east end of Princes St, head further east into Waterloo Pl, then about 300 m on the left side you come to the steps that take you up the hill.
It is a steady 5/10 mins climb up the stairs then a tarmac path way. It is really worth the effort as you get great 360 degree panoramic views of Edinburgh and its surrounding districts on a clear day, it also has to offer some great monuments of interest which form some of the most important landmarks of the city.
Calton Hill is one of Edinburgh's main hills, set right in the city centre. It is unmistakable with its Athenian acropolis poking above the skyline. The acropolis is in fact an unfinished monument - originally called the "National Monument" (nicknamed by locals Edinburgh’s shame!) Initiated in 1816, a year after Napoleon's defeat at Waterloo, it was meant to be a replica of the Parthenon in Athens, as a memorial to those who had died in the Napoleonic Wars.
It is home to some other famous historic monuments. The Nelson Monument, shaped like an up-turned telescope commemorates the death of Admiral Lord Nelson at the Battle of Trafalgar in 1805. However in 1852 a time ball was added to the top to enable ships moored in the Firth of Forth to set their time-pieces accurately. The City Observatory is also located here, a Greek temple styled building designed by William Henry Playfair in 1818.
Panoramic views of major landmarks can be seen from a bird’s eye view: Arthur’s Seat with the Crags behind Holyrood Palace and the new Scottish Parliament, Leith and the Firth of Forth, Princes Street in its New Town grid and the Royal Mile climbing up towards the Castle, also a great spot for enjoying the Edinburgh Festival & Hogmanay fireworks. The last day of April also sees the Beltane Fire Festival reviving an old Celtic tradition.
Calton Hill with its volcanic rockbase, gorse-strewn hillface and windswept ruggedness, it remains a rough gem.