The Pussywillows is a brothel located in King's Landing.
Penny Jenny took up residence at Pussywillows after the end of the First Blackfyre Rebellion. Here she raised her son and daughter. After her death, the other whores helped to raise the children. The daughter went on to be whore, whilst the son was knighted by Ser Morgan Dunstable and became Ser Glendon Flowers.
Glendon refers to the place as a tavern, to avoid people knowing that he was raised by whores in a brothel. Glendon is mocking referred to as the Knight of Pussywillows.