Edinburgh is a beautiful city with so much to see and do. Here's an ideal itinerary for 3 days in Edinburgh:

Day 1:

Start your day by visiting the iconic Edinburgh Castle, which sits atop a hill overlooking the city. You can take a guided tour or explore on your own. Afterward, head down the Royal Mile, a historic street that leads from the castle to Holyrood Palace. Along the way, you'll find plenty of shops, restaurants, and attractions to explore.

In the afternoon, visit the National Museum of Scotland, which has exhibits on Scottish history, culture, and science. If you're interested in art, check out the Scottish National Gallery, which has a collection of works by famous artists like Botticelli, Van Gogh, and Monet.

Day 2:

Start your day by exploring the charming neighborhood of Stockbridge, which is known for its independent shops, cafes, and galleries. From there, head to the Royal Botanic Garden, which has over 13,000 plant species from around the world.

In the afternoon, visit the Palace of Holyroodhouse, which is the official residence of the British monarch in Scotland. You can take a guided tour of the palace and see the State Apartments, where official ceremonies are held.

Day 3:

Start your day by taking a hike up Arthur's Seat, which is an extinct volcano that offers stunning views of the city. It's a bit of a climb, but the views are worth it!

Afterward, visit the Royal Yacht Britannia, which was the former yacht of Queen Elizabeth II. You can take a self-guided audio tour of the yacht and see how the royal family lived while at sea.

In the evening, catch a show at one of Edinburgh's many theaters, such as the Edinburgh Playhouse or the Traverse Theatre. Alternatively, head to one of the city's many pubs and enjoy a pint of local beer while listening to live music.

Overall, Edinburgh is a city with so much to offer, and this itinerary should give you a taste of its history, culture, and natural beauty.