1. Highly highly recommend the free walking tour (Sandemans) because you learn so much about the history of Edinburgh 2. Hike up Calton Hill for the sunset views (or any time of the day really) 3. St. Giles Cathedral to see the angel playing bagpipe sculptures 4. Walk around Greyfriars Kirkyard and find the names of some characters from Harry Potter on the gravestones (Hint: Tom Riddell, Moodie, McGonagall) 5. Spend a few good hours in a second hand bookstore to find some really cool Scottish books, music sheets...etc (Armchair Books, Edinburgh Books)