Here's an ideal itinerary for 7 days in Edinburgh:

Day 1: Arrival and Exploration

• Arrive in Edinburgh and check into your accommodation.
• Take a stroll down the Royal Mile, which is the main street in the Old Town of Edinburgh. You'll find plenty of shops, restaurants, and historical landmarks along the way.
• Visit Edinburgh Castle, which sits atop a hill overlooking the city. The castle has a rich history and offers stunning views of the city.

Day 2: Museums and Art Galleries

• Start your day at the National Museum of Scotland, which has exhibits on Scottish history, culture, and science.
• Next, head to the Scottish National Gallery, which houses an impressive collection of art from the Renaissance to the present day.
• In the evening, catch a show at the Edinburgh Playhouse, which hosts a variety of musicals, plays, and concerts.

Day 3: Nature and Parks

• Take a hike up Arthur's Seat, which is an extinct volcano that offers panoramic views of the city and surrounding countryside.
• After your hike, head to the Royal Botanic Garden Edinburgh, which has over 13,000 plant species from around the world.
• In the evening, take a stroll through Princes Street Gardens, which is a public park located in the heart of the city.

Day 4: Food and Drink

• Start your day with a traditional Scottish breakfast, which typically includes eggs, bacon, black pudding, haggis, and tattie scones.
• Take a food tour of the city, where you can sample local delicacies like smoked salmon, whisky, and shortbread.
• In the evening, visit one of Edinburgh's many pubs or bars and try some local craft beer or whisky.

Day 5: Day Trip to Stirling

• Take a day trip to Stirling, which is a historic city located about an hour's drive from Edinburgh.
• Visit Stirling Castle, which was once the residence of Scottish monarchs like Mary Queen of Scots and James VI.
• Next, head to the Wallace Monument, which is a tower that commemorates the Scottish hero William Wallace.
• In the evening, return to Edinburgh and relax at your accommodation.

Day 6: Shopping and Markets

• Spend the morning shopping on Princes Street, which is one of the main shopping streets in Edinburgh.
• Next, head to the Grassmarket, which is a historic market square that now has shops, restaurants, and bars.
• In the evening, visit the Royal Mile Market, which is a weekly market that sells handmade crafts, jewelry, and food.

Day 7: Final Day in Edinburgh

• Spend your final day in Edinburgh doing whatever you like! You could revisit some of your favorite spots from earlier in the week, or explore new areas of the city.
• In the evening, have a farewell dinner at one of Edinburgh's many excellent restaurants, and reflect on your wonderful week in this beautiful city.