1. Edinburgh is home to the world's largest arts festival, the Edinburgh Festival Fringe, featuring over 50,000 performances in more than 300 venues each year.

2. The Edinburgh Castle, one of the oldest fortified places in Europe, rests atop a 700 million-year-old extinct volcano.

3. Arthur's Seat, an ancient volcano and hill located in Holyrood Park, is a popular local hiking spot offering panoramic city views.

4. The Royal Mile, extending from the Edinburgh Castle to the Palace of Holyroodhouse, is actually one 'Scots mile' long, approximately 200m longer than an English mile.

5. The Balmoral Clock, a city landmark, is traditionally set three minutes fast to encourage locals to catch their trains on time at the neighbouring Waverley Station.

1. Visit Popular Spots: Don't miss visiting famous landmarks such as the Edinburgh Castle, the Royal Mile, Arthur's Seat, and the Palace of Holyroodhouse. Plan your day to avoid peak hours and consider purchasing tickets online to skip queues.

2. Save Money on Transport: Edinburgh's historic city center is compact and walkable, meaning you can save money on transportation. A hop-on-hop-off bus tour is also an affordable option to see the city, giving access to various points of interest throughout the day.

3. Dining Options: For a local culinary experience, head to Leith where you can eat at many award-winning restaurants, or try the local food in the Grassmarket and Victoria Street. If you're a fan of whisky, a visit to the Scotch Whisky Experience is highly recommended.

4. Timing Your Visit: Avoid the high tourist season and inflated prices by visiting during the months of April, May, and September when the weather is still pleasant, and the city is less crowded.

5. Itinerary Planning: Break down your visit according to areas of the city, like the Old Town, New Town, and Leith, to make the most of your time. Lastly, keep at least one day free to explore the beautiful Scottish Highlands, easily accessible from Edinburgh.