After visiting Alcazaba, I returned back to the city for a quick siesta to escape from the intense summer heat before returning uphill.
I discovered the views get even better above the Alcazaba at the Gibralfaro. Built during the Muslim era, the castle served as both a lighthouse and barracks, as well as to protect the Alcazaba. It has been restored and now contains a museum as well as lovely views from the ramparts at over 130m above sea level.
This historic map shows the old town and the fortresses just next to it on the right.
Note the Alcazaba and Gibralfaro are connected, as seen in this scale model.