Constantine doesn't need to be argued into your itinerary. It sits on a block of limestone cut off from the surrounding plateau by a gorge of the Rhumel River, and the city has been tying the two sides back together for about two thousand years. It was Cirta, capital of the Numidian kings, then a Roman colony that was destroyed in a civil war in 311 and rebuilt in 313 under a new name for the emperor Constantine. Ottoman beys ruled it from 1529, French troops took it in 1837, and in 1880 a French army doctor here, Alphonse Laveran, looked at a soldier's blood under a microscope and found the parasite that causes malaria.
Today it is a city of about 450,000 people, dramatic from every angle: a French-era downtown, an Ottoman old town clinging to the rock, and bridges from 1792 to 2014. It is also the home of the Constantine school of Malouf music. Three days is the right length: one for the rock itself, one for the bridges and the views, and one for Djemila, a UNESCO Roman town two hours away by road. Timgad, the other UNESCO Roman city, needs a fourth day.
Day one covers the museum, the palace and the old town, day two the bridges, the cable car and the evening music, and day three is the Djemila day trip. Start on a Sunday: Algeria's weekend is Friday and Saturday, so all three days are working days, and the cable car, reportedly shut on Fridays, should be running on day two. For the country as a whole, see Algeria. If you are also visiting the capital, 5 Days in Algiers covers it, and Constantine is roughly 320 km east of it as the crow flies.