Bressanone/Brixen is on the main line from Munich - Innsbruck - to Verona. There is even a through- train to Venice once a day. Sometimes there are specials for taking the train to Venice from Munich, so using one of these specials and getting off in Bressanone/Brixen is a lot cheaper than buying a regular ticket.
The train station is not in the old center of the town, but about 5 minutes walk up a hill.
For exploring Bressanone/Brixen it's best to walk. The old part is off-limits to cars anyway. Many alleys are really narrow, everything is close , so walking is your best choice.