The hop on hop off buses take you right to the front gate. At least that's how I arrived there. I'm sure Elizabeth II has alternate means of transportation.
Holyrood Palace, its adjoining abbey, and Holyrood Park are impressive. The Abbey which is now in ruins was built in 1128. The roof is gone, but that makes it an especially nice place to sit in quietness and watch the clouds go by.
The Palace was first built in 1501 and is what I would expect of a grand palace with thick, massive stone walls, huge rooms with heavy wood paneling, and bed chambers with ornate canopy beds. Mary Queen of Scots lived at Holyrood from 1561-1567. Her husband, Lord Darnley was apparently a jealous sort and suspected Mary of having an affair with her secretary, David Rizzio. One evening while she dined with Rizzio and several others, Lord Darnley and his friends burst into her room. They dragged poor Rizzio into another part of the apartment and stabbed him to death. Part of the Holyrood self guided tour takes you through the scene of the crime.
On a lighter note, the grounds of Holyrood Park are very peaceful. Sea gulls and terns make their home there and the wide open spaces have beautiful views of Salisbury Crags. I wish I had more time to explore the park. Beyond the cultivated gardens around the Palace are wilderness areas that are amazing to find in a city the size of Edinburgh. Apparently, Edinburgh has a greater percentage of green space than any other European capital.