Most city itineraries assume the days are interchangeable — that Tuesday and Thursday will look the same, so it hardly matters which one you give to the museums. Santiago's days are not interchangeable. The city sits in a basin pinched between the Andes and the coastal range, and what you can see from it changes overnight. On one morning the cordillera stands over the eastern suburbs in a wall of rock and late snow, close enough to feel like a set. On the next it is a rumour behind a grey lid, and the same viewpoint that would have justified the whole trip gives you a haze the colour of dishwater.
Everything Santiago does best from a height is worth doing on the first kind of day and close to worthless on the second. That single fact should organise your visit, and almost no plan accounts for it.
So what follows is not a sequence. It is two stacks of days — high days and low days — plus a fixed opener and a fixed exit. You decide which stack today belongs to while you are drinking your coffee, by looking east.
How many days the city is worth
Four. Three if you are tight, and the fourth is the one you will most regret cutting, because it is the day you leave the city altogether and let the Andes or the Pacific do the work.
Two days is not enough, and the reason is structural rather than snobbish. Santiago's best assets are spread across a basin roughly thirty kilometres wide: the colonial core in the centre, the parks and towers along the river to the east, the memory museums and old working barrios to the west, and the mountains and vineyards beyond all of it. Two days forces you to pick one axis and abandon the rest, and most people pick the historic core, which is — by common agreement among travellers who have seen more of Chile — the least distinctive thing here.
Five days is defensible if you are using the city as a base for a second excursion. Beyond that, you are better off spending the nights in Valparaíso or in the Casablanca valley and coming back.
The rule that sets the order
Check the mountains before you commit the day.
Santiago's air is at its worst in the austral winter, roughly June to August, when thermal inversions trap cold air under warm and the basin stops breathing. Spring and autumn are the recommended windows here partly for temperature and partly for this: the air moves again. In September and October the pattern tends to be a front coming through, a day of rain, and then a stretch of scrubbed, glass-clear air behind it — sometimes only a day or two of it, occasionally most of a week.
That clear stretch is your high day, and you should be ruthless about protecting it. Do not spend it indoors looking at ceramics, however good the ceramics are. Conversely, when the lid is down, the low day costs you nothing: a museum interior is the same in any weather, and the old barrios are arguably better in flat light.
One practical wrinkle that interacts with the rule: several of the things on the low day are closed on Mondays, including the pre-Columbian art museum, the memory museum and the San Cristóbal funicular, which shuts for maintenance at the start of the week and closes entirely on the first Monday of the month. If you land on a Sunday night, Monday is a high day almost by default — go up by cable car from the Providencia side instead of by funicular, and save the indoor work for Tuesday.