Edinburgh is a very impressive-looking place; more so than London, I'd say. It's built on the slopes of hills (around a castle of historic significance), and thus you have interesting things such as streets on different levels, entire streets going under other streets, buildings with two ground floors and lanes which are winding stone staircases. Which, as you can imagine, looks quite doovy.
A word of advice for visitors to Edinburgh: if you're keen on photography (or just nice views), go to Calton Hill. (Why doesn't every city have high hills with impressive neoclassical monuments in the centre?) If you're afraid of heights, ignore the preceding advice.
(Another word of advice: don't bother with those British Telecom Internet-enabled payphones. They're a nice idea, but the implementation leaves a lot to be desired. For one, the vandal-proof, payphone-style keyboards are impossible to type on at all comfortably, and the keys tend to behave somewhat erratically unless whacked with great determination. (And also the custom browsing software they use lacks certain amenities, such as, say, HTTP authentication. Haven't these people heard of Mozilla?))
That's what happens when you build a city inside an extinct volcano. :)