Cluj has three names and a long argument behind them. To Hungarians it's Kolozsvár, the town where King Matthias Corvinus was born in 1443 and the cultural capital of Hungarian Transylvania. To Germans it was Klausenburg, one of the Saxon trading towns. To Romanians it's Cluj, and in 1974 Ceaușescu added "Napoca", the name of the Roman town under it, to stress who had been here first. Locals of every kind just say Cluj. It passed from Hungary to Romania in 1918, back to Hungary in 1940 and to Romania again in 1944, and you can read that history in its squares, statues and churches if you know where to look.
Today it's the second-biggest city in Romania and one of its busiest: around 80,000 students, a tech industry that earned it the nickname "Silicon Valley of Romania", some of the best specialty coffee in the country and two big music festivals, Untold, one of the largest in Europe, and Electric Castle. It's also a perfect base for Transylvania: the Turda Salt Mine and gorge are 35 km away, and the Apuseni mountains and their villages just beyond.
Day one is Piața Unirii, the old town and the view from Cetățuia, day two the Ethnographic Museum, the Botanical Garden and the Romanian city around Avram Iancu Square, day three the Turda Salt Mine and Turda Gorge, day four the open-air museum in the Hoia forest and the history museum, and day five the white village of Rimetea under its mountain. For the rest of the country, see Romania and the guides to Sibiu, Brașov and Bucharest.