We were up fairly early on our second day in Edinburgh, and went for breakfast with our friends at a smally and lovely Italian café in the Grassmarket area - Caffé Piccolo was delicious! We could easily have lingered over coffee, but we wanted to get to the castle relatively early and hopefully avoid huge crowds. After climbing about a million steps up to the castle, we did have to wait in a queue for tickets and there was a big crowd, but as we realised later, NOT as big as the later crowd was.
We enjoyed the castle, especially the views of the city.
We were wondering about what appeared to be a Roman viaduct in the distance. A tour guide on a walking tour later in the week referred to it as the "shame of Edinburgh": an unfinished monument, but not a Roman ruin.
After our castle explorations we went for a coffee and treat on the Royal Mile before embarking on our Ghost & Underground Vaults walking tour. The tour lasts about an hour and is a pleasant way to see a bit of the city and learn a bit about its history.