Trentino-Alto Adige is a region made up by two provinces: Trentino around the city of Trento, and Alto Adige, or South Tirol, around the city of Bolzano. Alto Adige is officially bilingual: both Italian and German are spoken.
Trento was put on the map by the Consiglio of Trento the treaty between the papal power and the South german princes resulting in the contra-reformation. The local castle is a reminder of those days, with some nice murals (the best only by appointment) and boring furniture. There is also a cathedral and a diocese museum. But nicer is the modern art museum just outside the centre in a palace next to the river. It has changing exhibitions. Night life in Trento is rather boring, altough it is a university town, only few students sit around in cafes mainly on Via Verdi. The real fun they have is in the discotheques that are, strangely, located in the small villages, or along a minor roads. A car is required for these divertiti.
Bolzano has a few things more to offer. Some castles around the town, and Mr. Utschi, the glacier man, from long ago, around which a museum was build to show the life of early hunting-farming-gathering, European civilizations.
Other towns to visit are Merano, with baths, which sometimes has exhibitions at the Kurhaus, and Rovereto, with a nice pedestrian centre. First world war museums you can find in many towns, as this was the scene of a harsh mountain war in which many of the local Alpini Corp died.
But the real reason to visit Trentino-Alto Adige are the mountains, the Dolomiti, which are spectacular. It is possible to walk from May to half September, and ski from December to end March (give and take). The trains take you to Trento, Bolzano, Bressanone, etc along the main valley, but from there buses are regular and cheap, and will get you virtually everywhere, in the summer. In Trento the regional, blue buses leave from next to the train station.
If you are a bit experienced at mountain walking, you could try some via ferrata’s which are slightly more difficult walks with steel cables and ladder to secure yourself, bring a harness and perhaps a helmet.