That's an ambitious but doable schedule and, depending on how efficient your travel between places is, would afford you more time per city than a lot of people allot to those worthy places. I wouldn't call it a relaxing schedule, but it shouldn't be too uncomfortably rushed. Again, depending on how efficient your transportation turns out to be. Driving would make it efficient and flexible and allow you to linger a little longer or get on down the road as you wish. However, you may not want a car in any of those cities unless you stay on the edge and take public transportation into town. (I often do drive right on in, but then I used to live in Mexico and drove in the D.F.)

You probably already know that you need a reservation for the Alhambra. What isn't obvious is that the appointed time is not to enter the grounds at the gate but rather to enter the Nasrid Palaces within the Alhambra (which are the main point of interest for many people). You have a half-hour window to enter the Palaces or lose your reservation.