[The Saucepan Man]

Castle=fortified city/stronghold.

I disagree. A castle is a fortified building, not a fortified city. Cities may be built aroung castles, or they may be fortified themselves, as was the case with Minas Tirith, Minas Morgul and Edoras.

The only places falling within the traditional description of a castle in Middle-earth in the Third Age that I can think of offhand are the Hornburg at Helm's Deep, and the Tower of Cirith Ungol (which, although referred to as a tower, is more castle-like in its description). Orthanc and Barad-Dur come close, being fortified towers.