Edinburgh doesn't have a river flowing through its centre. It's not really coastal either so I guess it's quite unusual.
Never really thought much about it, but it is definitely true. Nearest river of any size is the Water of Leith which isn't really that close to city centre, and the city centre is about 5 miles inland from Leith (the port) which is quite a distinct place.
Most other cities seem to be one or the other. I guess it's because it grew up around the castle so is sort-of a hill top city. Like Macchu Picchu (sort of).