Next to the city hall/ Rathaus, there is a taller tower (called: Perlachturm) which you can enter to enjoy the amazing view over Augsburg and the surrounded nature. I visited the tower this afternoon, it costs 1,50 € for adults to enter the tower which you pay right before you enter the last level of stairs. The tower is open from first of May to the middle of October between 10 am and 6 pm. At the top, you can read about different landmarks and also use the binocular to get a closer look at buildings. The binocular is placed towards the church St Ulrich und Afra in the south. On the way up/down there are pictures of how the Perlachturm, the Rathaus and also other buildings looked like just during the end of World War 2 and after the war when the buildings was restored. Here is a link to leisure activities for tourists (or local citizens) in Augsburg.