This is where we currently live and I think it is the best city in the world except for the fact that it is so far away from family. Edinburgh is a modern city in old city clothes. The castle right on top of a hill in the middle of the city is like nothing you would find in the USA, but you have all the shops, restaurants, cafes, and entertainment you could want. I love the church communities and the little shops (if you can squeeze a stroller inside!). I love being to walk everywhere (except on rainy or snowy days). I love the free museums, the libraries, the history at every corner. I love experiencing the heart of Scotland yet mixing with international students at the University functions. I love the slower pace of life and the cultural differences that take me by surprise. And if you do come here, do the stereotypical stuff, like eating haggis. It really is part of the culture and all good fun.
If you decide to visit Edinburgh, I recommend Frommer’s “Edinburgh & Glasgow Day by Day” Guide book. It has all the good sites listed and described and includes a good fold out map. I still refer to this book even after living here for two years.