The customs house is a large building in the centre of - or, according to Nathan Drake's map, in front of - the drowned city. It is a large dome shaped building with an orange, severely damaged roof. The house overlooks a large body of water, and can be seen from the Fortress.
A large group of Eddy Raja's pirates were occupying the building when Nathan Drake and Elena Fisher arrived. Inside, Nate and Elena discover a library of old ship manafests, as well as the log book.