Whenever you go and Travel somewhere, you usually need a place to stay. Even if it is just to get some shut eye, it is good to have a safe place for the Night.
And when you are on a Budget, nothing can beat a Hostel. And here in Germany, I usually prefer to stay at the Jugendherberge, even though they usually do cost a few Euros more per Night.
Off course you would need to be okay with Strangers sleeping in the same Room. But I usually have no Problems with that, depending on the People and how they behave. Being a Douchebag in a Dorm Room is never a good Idea.
Usually, Jugendherbergen are also located quite nicely. Like in Mannheim and Cologne, where they are right at the Rhine. Or in Hamburg, where the JH sits right above the Landungsbrücken on the Stintfang, Hamburgs only whine yard.*
Another important Thing for a day of Exploring is a good Breakfast. And usually, the Jugendherberge provides. Sometimes, they also allow you to pack yourself a Lunch Bag, but it is better to ask in advance.
You can also meet likeminded People at the Jugendherberge. Most People who stay there are either School Kids or Explorers. And School Kids are usually not allowed at the JH Bar.
The only downside is that you need to be a Member of the Jugendherberge, without that, it costs a little more per Night. The good thing is that that Membership also doubles as a Hosteling International Membership, as the Jugendherberge is Germany’s Hosteling Association.
*there are two more Jugendherbergen in Cologne, one at the Train Station, and one opposite of the Fair Grounds near the Hohenzollernbrücke. Also, I have no affiliation with the Jugendherberge.