The old town is compact enough to walk entirely, and most of what you want to see is within fifteen minutes on foot. The Stone Bridge, the cathedral, Saint Emmeram's Abbey, and the Scots Monastery are all in the historic core. Cycling is popular — Regensburg sits on the Danube Cycle Route (EuroVelo 6), and the riverbanks are easy cycling territory.
The city has a reasonable bus network for reaching outer districts and the university, but you rarely need it as a visitor. Bike hire is available from several points near the old town. The Hauptbahnhof is a short walk south of the historic centre.