The old man looked around nervously searching for his hat.
Literal
Grandfather [topic-は] hat [object-を] searching surroundings [object-を] restlessly looked-around.
きょろきょろ is a 擬態語 for looking around restlessly — eyes darting in different directions. 見回す ('to look around, survey') is a compound verb. The mimetic adds a visual quality that makes the scene vivid.