The best way to see Edinburgh is to get lost in the city. There are many winding, narrow back streets to explore. Just walking around in the city is amazing.
While taking your walking tour, stop in at the Elephant House. This is a funky little coffeehouse right on your way to Prince's Street.
Take a walk up the hill by the Divinity School at the University of Edinburgh. There is an impressive view that looks down on the Royal Mile.
Quick Tips:
Don't bother with an umbrella. You will notice that most Scots either brave the rain, or invest in a sturdy raincoat. If you try to fight back the rain with an umbrella, it will be ripped apart by the wind.
Best Way To Get Around: