In the books
In the A Song of Ice and Fire novels, Starfall is the seat of House Dayne. It is located at the mouth of the River Torentine, downriver from Blackmont and the High Hermitage, which is held by a lesser branch of the Daynes.
Starfall is so-called because of a meteor which fell out of the sky nearby, almost two thousand years ago. The Daynes forged a sword out of the meteorite ore, called "Dawn", which is as resilient and formidable as a Valyrian steel weapon in combat. Only the most skilled and honorable knights of House Dayne are entitled to wield Dawn in battle; such paragons are given the title 'Sword of the Morning'. The last Sword of the Morning was Ser Arthur Dayne, one of King Aerys II Targaryen's Kingsguard, who was killed by Eddard Stark during Robert's Rebellion. Eddard returned Arthur's bones to his sister, the Lady Ashara Dayne, at Starfall. Ashara cast herself into the sea from the Palestone Sword, a tower at Starfall, in despair at the news of her brother's death.
House Dayne is a fairly important house in the novels, but has not been mentioned in the TV series so far.
- Starfall at A Wiki of Ice and Fire (spoilers from the books)