The woman is:
Revelation 17:18—
And the woman whom you saw, is that great city which reigns over the kings of the earth.

(Map From Unger's Bible Dictionary, page 934)
She sits on seven mountains (hills).
Revelation 17:9—
And here is the mind which has wisdom: The seven heads are seven mountains on which the woman sits.

The Basic Everyday Encyclopedia page 451 gives us the following information concerning these seven mountains (hills).
Rome (the "Eternal City"), ... Traditionally founded 753 BC by Romulus and Remus, built on 7 hills...

Compton's Pictured Encyclopedia, 1948, Volume 12, page 144, also tells us about the city of seven hills.
...the "City of Seven Hills." ...the Capitoline, Palatine, Aventine, Quirinal, Viminal, Esquiline, and Caelian hills. ...the seat of the papacy, the head of the great Roman Catholic Church.

The waters are explained in:
Revelation 17:15—
And he said to me: The waters which you saw, where the whore sits, are peoples, and multitudes, and nations, and languages.