It’s a long walk from the Generalife to the alcazaba and the Nazrid Palaces. It’s nicely landscaped and their are ruins of what was once a town along the way. Also one of the few cats we saw.

Alhambra tickets and logistics
The Alhambra is huge and a variety of tickets are available. We purchased the 72-hour version of the Granada Card which included all parts of the Alhambra, several other local sights, and nine bus trips. We didn't see all the sights (we hit most of them) or use all the bus trips and still felt it convenient and cost effective. To see the Nazrid Palaces (which you should) you need to choose a date and time as access is limited. We found the Love Granada website very useful in planning our visit to Granada.
In and near the alcazaba are nice overviews of the city and surrounding mountains.
The museum is a newer building. No one is quite sure what’s up with the circular structure, or whether it was meant to have a roof. If you need to skip part of the Alhambra, this is the part to skip.
The gardens here are between the alcazaba and the palaces.
More of the beautiful gardens surrounding the buildings.
Some very linear water gardens.