Longbow Hall is a castle located in the Vale of Arryn. It is located south of the Fingers east of Heart's Home and north of Old Anchor. It appears to be located in the foothills between a mountain range and the east of the valley.  It is the seat of House Hunter.
In the books
In the A Song of Ice and Fire novels, Longbow Hall is the seat of House Hunter, a vassal of House Arryn.
The Vale of Arryn