Casterly Rock:
Nicknamed the Rock, it is a fortress and the seat of House Lannister. The capital of the Westerlands, it overlooks the harbor of Lannisport and the Sunset Sea. The fortress is carved out of a great stone hill and its natural defenses are further enhanced with walls and other structures. It is tunneled through with halls and chambers, with a huge keep at its peak. Gold-producing mines are possibly still productive in the hill. Nearby strongholds include Kayce and Feastfires to the west, Sarsfield to the north, and Cornfield and Clegane's Keep to the south.
Three key rooms within the Rock are the Golden Gallery, the Lion's Mouth and the Hall of Heroes, where the Lannisters and their close kin who have died valiantly are interred. From below the Rock thunder can be heard, where the sea comes in. In the bowels of the Rock are rooms where caged lions were once kept, and cells for the worst prisoners. There is a place called the Stone Garden within the castle; it contains a weirwood a tenth the size of Raventree Hall's.
Legend says that Casterly Rock is named for the family that ruled it in the Age of Heroes, the Casterlys, who no longer exist. The Lannisters trace their rule over it back to Lann the Clever, who tricked the Casterlys out of their castle and claimed it for his own. Some claim that Lann still haunts the castle. After Daenerys' coronation, the house was on rocky territory with the new queen for their part in Robert's Rebellion, assassination attempts on Daenerys, and the near ruin of the Seven Kingdoms under Cersei's regime. They have since recovered and even have a member on the council.
Lannisport:
Lannisport is a walled city ruled by House Lannister of Casterly Rock, which is just north of the city. Lannisport is located along the coast of the Sunset Sea where the river road, the gold road, and the ocean road meet. It is one of the major ports of the Seven Kingdoms and is the largest settlement in the Westerlands. The Lannisters anchors their fleet in its harbor. The city is renowned for its goldwork. Lannisport is policed by the well-trained City Watch and is home to the cadet branch House Lannister of Lannisport and distant kin to the Lannisters like Lannys, Lannetts, Lantells, and other lesser Lannisters, many of whom are yellow of hair.