Edinburgh has a great transportation system, consisting of buses and trams. The Edinburgh Trams operate with stops in the city center, including directly to Edinburgh Airport. The cost of a single ticket varies depending on the travel zone but generally costs around £1.70 - £2.20, with day tickets and multi-day tickets also available. Taxis are also convenient but can be more expensive. Walking is a great way to explore the city, and most attractions are within walking distance of each other.
If you have more time, consider taking a day trip to nearby attractions such as St. Andrews or Loch Ness. For a shorter trip, consider skipping one of the attractions such as The Real Mary King's Close or The Scotch Whisky Experience. The city offers a lot of free activities, such as visiting the Royal Botanic Garden Edinburgh or hiking up to Arthur's Seat. Additionally, be prepared for the weather and bring layers, as it can change quickly.