Start at the Old Town. It contains the Royal Mile and Edinburgh Castle as well as most of the city's other renowned tourist sights. Since the Old town is roughly a mile long, walking distances won't be a problem, even though some of the going will be uphill.
Visit Edinburgh Castle, and allot plenty of time for a tour once inside. One can take a guided tour or select an audio tour instead.
Look for ghosts at Mary King's Close, also in the Old Town. Schedule ahead for a tour for this part of town, as visitors aren't allowed to wander the close in streets of old on their own, and the tours tend to fill up fast on certain days.(See Resources below.)
Find time in the day for a lunch break. Edinburgh boasts many wonderful restaurants and pubs. Asking a local is often a good way to find a tasty meal.
Queen Elizabeth's Scottish home is at the end of the Royal Mile. The Palace of Holyroodhouse can be toured as long as the queen is not in residence. There's even a café in the Palace's Mews Courtyard.
