The old town of Augsburg can be walked. You can reach all main sights and the train station on foot. Do not, however, underestimate the distances.
Wealthy and powerful Augsburg covered quite a lot of ground even centuries ago. The old town is large. If you want to visit, for example, the cathedral, the Fuggerei and St Ulrich and Afra and return to the train station, you'll walk a considerable distance. Wear comfortable shoes. Allow enough time.
People who have difficulties walking are advised to get a day ticket and use public transport as hop-on-hop-off to save themselves some kilometres.
DO NOT go to Augsburg on SUNDAY as many things are closed. First, the main pub I wanted to visit was closed down permanently and then this place that I had chosen for lunch was closed on Sundays. It's called the Goldener Gans Braustubbe and is at Weitgasse 11. It is proported to have excellent food and is the brewery tap for Goldener Gans, the oldest brewery in Augsburt (1346). Luckily, right up the street on Weitgasse was a Hasenbrau outlet that I described in my memory.