Jamieson, Fausset and Brown on Daniel 4:29

29. twelve months--This respite was granted to him to leave him without excuse. So the hundred twenty years granted before the flood (Ge 6:3). At the first announcement of the coming judgment he was alarmed, as Ahab (1Ki 21:27), but did not thoroughly repent; so when judgment was not executed at once, he thought it would never come, and so returned to his former pride (Ec 8:11).

in the palace--rather, upon the (flat) palace roof, whence he could contemplate the splendor of Babylon. So the heathen historian, Abydenus, records. The palace roof was the scene of the fall of another king (2Sa 11:2). The outer wall of Nebuchadnezzar's new palace embraced six miles; there were two other embattled walls within, and a great tower, and three brazen gates.