Personally, I think this is one of the most beautiful squares in Italy, where you'll find the Cathedral of San Vigilio. At the centre is the Fountain of Neptune, built back in the eighteenth century. Piazza Duomo is more than the geographic nerve centre of the city; it's also an important point for get-togethers. There's a market, and plenty of events take place here.
Rasmo square is another of those incredible spots that the city of Trento offers visitors. You can get there by following Via del Suffrage to the junction with Via Manci. You'll find the Piazzetta a little further on - a place of peace and tranquility with a couple of tables. It is at its most beautiful in December, when it is lit up with Christmas decorations. You will come out in the open space near Torre Verde and Buonconsiglio Castle.
With a beautiful view of the tower that rises from Piazza Duomo, Piazza Pasi is one of the prettiest squares in Trento. It's always very popular because of its namesake bar, which is frequented by young and old alike. From here it's easy to get to the Teatro Sociale and the library in Via Oriola.