One thing you need to know, you always hear people talk about the Alcazaba, but really there's two fortifications that actually do require separate entrance. The Gibralfaro is the castle that sits higher on the hill, while the Alcazaba sits lower on the hill. Though connected by castle walls, there is no way for visitors to go from one to the other internally. Since we got a late start and weren't exactly sure where we were going, we ended up doing them on different days. We started with the Gibralfaro, which might very well have been the prettiest part of the entire trip.
Once inside, you could pretty much explore everywhere, much like we did at the St. Goar castle, except the weather was actually nice. Though not as dangerous or secretive looking, there were still stairways that you were never quite sure if they would continue through, but they always did! You could also walk along the walls, which is always exciting. It gives you good views of the inside of the castle as well as the views of the city and landscapes beyond. And it gives you that wonderful feeling of being able to walk the paths of people long ago.
Entrance Cost: 2.10 € or 3.45 € when purchasing a Gibralfaro/Alcazaba joint ticket (must be used within 24 hrs of each other)
Hours: Tuesday-Sunday, closed Mondays
Time to self-tour: 1.5 hours
Walk up to castle: 20-25 min
Total Time with the Alcazaba: 3-4 hours (including walks up to and from one to the other because the Alcazaba and Gibralfaro do NOT connect inside)