The unnamed Baelish Castle is a castle in the Vale of Arryn. It is the seat of House Baelish, a recently established House that once held fealty to House Arryn of the Vale before the War of the Five Kings. House Baelish was founded by Petyr Baelish's great-grandfather, a common sellsword from Braavos, and it was his son (Petyr's grandfather) who was awarded the small keep the most minor of lordships, just a few stony acres in the northernmost and smallest of the peninsulas known as The Fingers.
House Baelish is now one of the major houses, being formerly the ruling house of The Riverlands, and currently the ruling protectors of the Vale. The castle is located north-east of the Eyrie, on the smallest of The Fingers' peninsula on the coast of the Narrow Sea. The castle has no official name. 
The current head of House Baelish and Lord of Baelish Castle is Petyr Baelish, great-grandson of a Braavosi sellsword who founded House Baelish, and grandson of a hedge knight who was rewarded the castle. There is no maester appointed to the castle, and was never given an official name.
In House Baelish Histories & Lore, The Fingers and the castle are described as "four rocky peninsulas plagued by wind and rain and barren to all but the hardiest of weeds, the ancestral home of House Baelish... a small tower on the gull-stained rocks of the Fingers". It was revealed that Petyr Baelish did not enjoy his childhood there, and described his fathers efforts to allow him to be fostered at Riverrun as "heroic".
In the novels
In the A Song of Ice and Fire novels, Sansa actually visits Baelish Castle briefly, as it is the first place she and Littlefinger land when they arrive on the coast of the Vale, after escaping from King's Landing. She then proceeds from there to the Eyrie, but the TV series simply skipped this.
The castle is an old flint tower, located on the smallest of the Fingers. A staircase winds around the inside wall, and each floor has only one room. The ground level houses servants and dogs in the kitchen, the middle floor is a hall, and the third floor contains the bedchamber. It has arrowslits for defense but no windows. A shield depicting the Baelish titan's head hangs above the hearth.
The vicinity includes a flock of sheep, a village of a dozen families. There is no safe anchorage nearby for large ships.
In conversation with Sansa Stark, Petyr Baelish denounces the castle and gives it the derogatory names "Sheepshit" and "Drearfort".
- ↑ House Baelish (Histories & Lore)