Rome is devided by the Tiber river. In the eastern part there is the historic Center and the seven hills on which the city was originally built. In the western part you will find Vatican City and Trastevere, amongst other districts.
You could argue that the Pantheon is exactely in the center of Rome and thereby reference point for orientation. Almost everything that is interesting for visitors lays in a 1-mile-radius from the Pantheons.
The Tiber river itself is not very wide and is crossed by many historic bridges. Between Centro Storico and Trastevere there is a picturesque island in the river.
Few cities have as many systems as Rome for naming and organising their districts and neighbourhoods. The official district names for example are not really part of every day's life, instead centuries old nomenclature for quarters are still in use. There are also dozens of opinions on what belongs to the "historic center" in a city almost 3,000 years old.