Bologna is the Italian city that doesn't need to shout. It has the oldest university in the world still teaching, founded around 1088, and for centuries the city lived off its students: it built porticoes so that the crowds of newcomers had somewhere to live and walk in the rain. There are more than 38 km of them in the historic center, and in 2021 UNESCO put them on the World Heritage list. The Two Towers are still the symbol on every postcard, though one is fenced off and the other can't be climbed. More on that on day two.
It's a city to walk slowly and eat in. It won't hit you with one monument the way Florence does with its dome; it adds up. A basilica with an unfinished facade, an anatomical theatre carved in wood, market lanes where the same shops have sold ham and cheese for generations. Four days is enough for the center. The fifth is for a day trip, and Bologna's trump card is that Modena, Parma and Ravenna are all about an hour or so away by train. This guide spends that day in Modena and explains why Parma and Ravenna didn't get it.
The plan keeps every day in one part of town. Day one is Piazza Maggiore, San Petronio and the market lanes of the Quadrilatero, day two the Two Towers, Santo Stefano and the Seven Churches, day three Modena, day four the university quarter and the long portico walk up to San Luca, and day five the markets, the hidden canal windows and a view from the hills. It chains well with 5 days in Florence and 5 days in Venice, both under two hours away by fast train, and with 5 days in Verona and 5 days in Milan on the same northern rail corridor. Start on a Tuesday if you can: Monday closes the Pinacoteca, the Collezioni Comunali and most of Santo Stefano, and Sunday closes the Archiginnasio and the Mercato delle Erbe shops. There's more about the country in our Italy page.