Lannisport

Lannisport is a large city located on the west coast of Westeros, on the Sunset Sea just south of Casterly Rock, the seat of House Lannister. A cadet branch of the Lannisters rules the city in the name of Lord Tywin Lannister. It is a bustling seaport.

Season 1
Whilst trading barbs with Theon, Tyrion Lannister reminisces about the occasion during the Greyjoy Rebellion when Lannisport was attacked by the ships of House Greyjoy. Lord Balon Greyjoy's two brothers burned the Lannister fleet as it sat at anchor, prolonging the war until Lord Stannis Baratheon was able to bring the Royal Fleet around from the east coast of Westeros and smash the Greyjoy fleet in open battle. Tyrion recalls seeing sailors burning.

In the books
Lannisport is located just south of Casterly Rock and is a large and bustling seaport with a population of approximately 300,000, making it the third-largest city in Westeros, after King's Landing and Oldtown. Cersei Lannister and her friends used to sneak into the city whilst young to see the sights.