Despite not having all the ornamentation of the other parts of the castle the Alcazaba had the best views beyond a shadow of a doubt. I mean, it makes sense that it would because if you are trying to defend the castle you need to be able to see! This is the place where we took a panorama and could see most of the city and the Albayzin.
There isn't a whole lot to the Alcazaba beyond the defenses but it still takes a fair amount of time to go through if you want to see it all. There are a couple towers to climb and you will definitely want to stop and take in the views. The best view in my opinion is looking back towards the mountains past the rest of the Alhambra, seeing palm trees growing within the castle, feeling the heat and through all this seeing in the background a snow capped mountain!
Visiting Information near bottom of this page.