There is a wee bit more to the city than the medieval section; the world heritage site covers both old and new towns.
The New Town is a great example of Georgian town planning dating from the 1760s (photo below shows both towns). Though a lot of the photos of Edinburgh focus mainly on the old town, with a few New Town Buildings like The Balmoral Hotel included, there are some interesting parts to the New Town and West End too. For instance there is Moray Estate
Unfortunately, the New Town gets overlooked, despite it being slightly bigger than the Old Town; and is a bit less overrun with Tourist shops too.