As I live in Germany I'll have to recommend somewhere from here. There are many picturesque towns which are must-sees, but they are small ans each one on its own wouldn't warrant a five-day stay. But there are many close to each other and public transport is good, frequent, and affordable. Rothenburg on der Tauber is a typical town to start from.
Also there is Freiburg which is very popular and has lots to offer. From there you could take in Basel and some beautiful countryside.
Strasbourg is also ideal, with many towns nearby worth looking at. The French are really good at adorning their streets with flowers.
An area I don't know well, but can imagine you could walk for miles would be the North Sea coast. Bremen is a charming town. The Baltic coast has even more to offer, and you could alternate beach walks with city streets in both of those. For the Baltic side, start from Hamburg or Lübeck. Fascinating history as the Romans didn't get up that far, so it's more about the Slav and Viking periods.