City center can be covered by foot (depending on your fitness, etc). Look for the red line on the pavements - so called "red walk" which connects nearly all the attractions within the centre. This is by far the best way to discover the centre on foot, as all attractions are marked by a number (there are about 40) on the pavement, so you won't miss one. At each of them there is a sign explaining some details about the sight.
The red line starts and ends at the train station. When you exit through the main entrance, turn left on the sidewalk and look for it, some of the paint may have already vanished. Close to the start is also a map showing the route and the attractions. You can get a similar map that also includes the red line at the tourist information center.