Most travellers give Granada a single day, and the Alhambra takes all of it. Tickets go on sale months ahead and sell out; the half-hour slot printed on yours decides when you get up, where you eat, and how far you are willing to wander beforehand. It is a magnificent day. It is also a day in which you see almost nothing of the city the palace looks down on.
The second and third days are where Granada stops being a monument and starts being a place, and they are unexpectedly easy to arrange. Almost nothing below is timed. Almost nothing sells out. A surprising amount of it costs nothing at all, and the rest is cheap enough that a whole third day can come in under the price of one Alhambra ticket. Spring is the season on record here, and it shows: snow still sitting on the Sierra Nevada behind the Albaicin rooftops, the walled gardens in flower, the courtyards not yet baking.
What follows is ordered to spare your legs, which in Granada matters more than it sounds.
The Albaicin has interiors, and hardly anyone goes inside
The Albaicin is the most photographed neighbourhood in Granada and one of the least entered. Visitors climb it, point a phone at the Alhambra from the Mirador de San Nicolas, and come back down having opened no doors. Behind those whitewashed walls sit half a dozen Nasrid and Morisco houses, and between them they tell you more about how Granada actually lived under the emirate than the palace does.
Start low, on the Carrera del Darro, at El Banuelo. These are eleventh-century Arab baths, older than the Alhambra by a long way, and what survives is the bare architecture: brick vaults pierced with star-shaped skylights, columns reused from earlier Roman and Visigothic buildings. Ten minutes uphill, the Casa de Zafra is a late fourteenth-century Nasrid house built around a pool and a portico, given away to the Catholic Monarchs' secretary after the conquest and now doubling as the neighbourhood's interpretation centre. It is the clearest surviving picture of a wealthy Granadan home of the period. The Casa Morisca del Horno de Oro is a smaller, more domestic version of the same idea.
Keep climbing to the Palacio de Dar al-Horra, tucked behind the old city wall near the Convento de Santa Isabel la Real. It was the residence of Boabdil's mother, and its upper gallery gives you the Albaicin from inside the Albaicin rather than across it, which is the rarer view. The Casa del Chapiz, higher again on the edge of Sacromonte, now houses a university institute for Arabic studies; its gardens look straight across the ravine at the Alhambra's north wall with no crowd in front of you.
All of these, plus the Corral del Carbon down in the centre, are sold together as the Dobla de Oro. The headline version bundles a night visit to the Nasrid Palaces and runs to around EUR 30 at the time of writing, which is not what you want on a second day. There is a cheaper ticket covering only the Andalusi houses, and the houses also sell entry individually for a few euros each. The Corral del Carbon is free: a fourteenth-century merchants' inn with a horseshoe-arched gateway, sitting unremarked a two-minute walk from the cathedral, and quite possibly the single most overlooked building in the old centre.
One more Albaicin door, and it costs nothing: the Casa-Museo Max Moreau, the house of a Belgian painter who settled here, kept as a carmen with its terrace intact. Carmen is the local word for a walled house-and-garden, and this is the easiest way to stand inside one. It typically opens mornings and late afternoons from Tuesday to Saturday, closes on Sundays, Mondays and public holidays, and shuts for the whole of August, so check before you climb.
A note on the Mirador de San Nicolas: at sunset it is a scrum, three deep, with buskers. The Placeta de Carvajales, a few minutes away, gives you nearly the same composition with a fraction of the people.