"He then climbed out of the portrait hole, up through the silent castle (held up only briefly by Peeves, who tried to overturn a large vase on him halfway along the fourth-floor corridor), finally arriving at the Owlery, which was situated at the top of West Tower."
The West Tower is one of the towers of Hogwarts Castle. It houses the Owlery and is located thirteen windows to the left of Charms professor, Filius Flitwick’s office.
In PA, Sirius Black is locked in Professor Flitwick's office, which is thirteen windows to the right of the West Tower. The hippogriff, Buckbeak, flies up to the tower in PA21, carrying Harry and Hermione, to save Sirius and help him escape.
The Owlery, where the school owls and the owls belonging to students live, is located on the top of West Tower (GF15).
The Owlery was a circular stone room, rather cold and drafty, because none of the windows had glass in them. The floor was entirely covered in straw, owl droppings, and the regurgitated skeletons of mice and voles. Hundreds upon hundreds of owls of every breed imaginable were nestled here on perches that rose right up to the top of the tower, nearly all of them asleep, though here and there a round amber eye glared at Harry. He spotted Hedwig nestled between a barn owl and a tawny, and hurried over to her, sliding a little on the dropping-strewn floor (GF15).
Because the Owlery has has glassless windows, the winter elements get into the tower. This means that students and other visitors of the Owlery have to be careful of the icy steps.