Edinburgh has 7 of Scotland's 10 most visited tourist attractions:
Edinburgh Castle
Royal Botanic Gardens
Royal Museum of Scotland
National Gallery of Scotland
Edinburgh Zoo
Scottish United Services Museum
Holyrood Palace
If that's not enought, there is also:
The 'Old Town' around the High Street
The 'New Town' from Princes Street northward
Scottish National Gallery of Modern Art
Museum of Childhood
City Art Centre
If you are planning to visit edinburgh, it is generally accepted that you should try to see:
Edinburgh Castle
The Royal Mile and Holyrood Palace
Edinburgh Military Tattoo (every August)
Edinburgh Festival (from mid August to the first week of September)
The Royal Mile and Holyrood Palace
Royal Academy of Scotland Art Gallery
Fantastic shopping on Princes Street
Royal Yatch Britannia