You can overlook the city from this castle.
見渡す is a very natural expression. And 眺める（ながめる）is completely interchangeable with 見渡す in this context.
見渡す consists of 見る (to see/look at/watch) + 渡す (to bridge/to hand over ==> from here to there ==> throughout).
眺める has several meanings: 1) overlook (a broad space); 2) take a close look at something; 3) wait and see (i.e. try not to involve oneself in a complicated situation); 4) take in a scenery in a reflective mood. The Japanese sentence is interpreted as 1).