There are many options on where to stay in Edinburgh, from small Bed & Breakfasts, to newer contemporary design hotels to more traditional properties.
94 DR: Edinburgh has wonderful guest houses. This a great spot south of the old town near the University. Paul and John, the owners, have created a very contemporary, upscale spot with beautifully furnished rooms and great breakfasts in the conservatory overlooking the garden. Their knowledge of the area, particularly relating to restaurants was great! Thanks guys for a great experience!
For a hip, contemporary hotel you should consider the Royal Mile Edinburgh (formerly Missoni Hotel). Also on the Royal Mile is the contemporary Radisson Blu. For something more traditional you can pick the Caledonian, which is now a Waldorf Astoria Hotel, where I stayed on his first trip to the city in 1972 with my parents.
We have also recently read about the upscale boutique hotel, No 11 Brunswick Street, in a Georgian rowhouse. There is also the Nira Caledonia and the renovated Glasshouse Hotel which was just featured in the New York Times. Also check out The Scotsman, a boutique hotel. It is very traditional with an attractive lobby and restaurant in a great location.