1. Orient Yourself
The first step to enjoying this city is orienting yourself with local landmarks and well-known spots around town. The most notable places to start are Princes Street and the Royal Mile. And trust me, those are great places to begin. Edinburgh is the only successful Garden City in the world that has been undertaken in the modern age. So get out and explore the truly amazing sites.
2. Find Yourself a Nice Pub
This is crucial to a proper Scottish experience. Finding a pub/bar you like will remove up the "outsider looking in" feeling in favor of a more relaxed persona. My favorite pub on Rose Street is called Milnes Bar and is by far the best I've come across!
3. Take a Stroll through Princes Street Gardens
Walking through the gardens is one of my favorite things to do in the city. You will see the dichotomy of the old town on the hill and the new town down below. The difference is striking and something your are surely never to forget!
4. Sample Mulled Wine from the Christmas Markets
Although Edinburgh cannot compare the the Viennese Christmas, they will still gladly warm your up with a spiked cider or a warm mulled wine and maybe even some haggis bon bons is you're lucky!
5. If Nothing Else...
Try and find a place in the city where you feel at home, and trust me, it's not too hard. Whether it's a cafe, restaurant, book shop or park, Edinburgh is waiting for you.