Things to do in Edinburgh
Try http://www.edinburgh.org/events/ - For a guide to what's on - lots of things to do in Edinburgh
History - all around you ; the Castle, Holyrood Palace; The Royal Mile and the Old Town, the Georgian New Town
Fresh Air : Visit the world class Botanic Gardens - fabulous in May; walk up Arthurs'Seat for a panoramic view of Edinburgh; Climb the Scot Monument; take the train to North Queensferry to see the Forth Bridges; pop down to the waterfront at Leith.
And Edinburgh's so small there's no excuse not to do it all !