Three days is the standard Cajamarca trip, and it is enough, provided you do not try to reach both Cumbemayo and the Lagunas de Alto Peru in the same window. The sequence below acclimatises you first, puts the high excursion in the middle, and keeps the last morning flexible for a flight out.
Day one: the city, slowly
You are at 2,750 metres and you arrived today. Do not climb anything yet.
Morning or afternoon of arrival. Walk the Plaza de Armas and go into the Cathedral and the Iglesia San Francisco. Both are on the square, both are free or nearly so, and the carved facades are the best colonial stonework in northern Peru.
Then the Cuarto del Rescate, the Ransom Room, two blocks off the plaza. It is one small stone chamber and it takes twenty minutes, but it is the room where Atahualpa was held after the 1532 ambush, and it is the only Inca building still standing in the city. Read the site before you go; the interpretation on site is thin.
Late afternoon: Conjunto Monumental de Belén. The church, the old hospital buildings, and the small archaeology and ethnography museums, all in one ticket.
Evening. Eat around the plaza. Sleep early. The first night at altitude is usually a poor one.
Day two: Cumbemayo
This is the day that justifies the trip, and it needs a full morning.
Cumbemayo sits at about 3,500 metres, roughly 20 km southwest of the city on a rough road. The site is a pre-Inca aqueduct, canals cut into volcanic rock around 1,500 BC and still running, set in a "stone forest" of eroded pillars, with petroglyphs along the channel.
Organised half-day tours leave from the plaza in the morning and are the practical option; the road is bad and the site is not signposted for independent visitors. Take a jacket regardless of the forecast. It is consistently cold and windy up there.
Afternoon: Baños del Inca. The thermal complex is 6 km east of the city and a short combi or taxi ride. These are the hot springs Atahualpa was using when Pizarro arrived, and after a morning at 3,500 m they are exactly what the day needs. Pay for a private pool rather than the public one; it costs very little more.
Day three: the valley, then out
Morning: Ventanillas de Otuzco. Eight kilometres from the city, a cliff face honeycombed with pre-Inca burial niches. It is a short visit, an hour plus travel, and it pairs naturally with a stop at a dairy farm on the same road.
Then Cerro Santa Apolonia if you have the afternoon. The stairs up from the city centre take twenty minutes and end at the carved stone seat known as the Inca's Throne, with the whole valley laid out below. Best in late afternoon light, and by day three the climb will not bother you.
If your flight is early, cut Otuzco and do Santa Apolonia the evening before instead.
If you have a fourth day
Take it into the countryside. Granja Porcón is a Quechua co-operative forestry project with vicuñas and rescued spectacled bears, about an hour and a half out. Lagunas de Alto Peru is higher, wilder, and the best walking in the region, but it needs a full day and an acclimatised body. Cuntur Wasi, further west, holds gold work from a culture older than Chavín and is the strongest archaeology in the department.
What to skip if you are short
The city museums duplicate each other. If you only have time for one, make it Belén. And do not attempt Cumbemayo and Alto Peru on consecutive days unless you are already comfortable above 3,500 metres.
