Hiking Germany

The first place I would suggest is Oberstdorf, in Bavaria. Oberstdorf is a major German ski area with plenty of rooms. It is at the base of the Austrian Kleinwalsertal, a beautiful Alpine valley full of hiking trails. I know of a lot of Germans that go there every year for three weeks and spend their time hiking in the mountains. Sometimes they ride the ski lifts up and hike down. The is a regularly schedule bus from Oberstdorf into the Kleinwalsertal.

Another place would be in the Harz Mountains, a German national park. A know there are organized hikes there where you hike to a different town each day and the tour company takes your luggage to the pre-arranged lodging in the next town. And you end up at the end of the week back in the starting town.

Several places in the Black Forest fit the bill. Neustadt-Titisee is one. Check out some videos on Youtube by Ranier Dornburg.

The Taunus mountains north of Frankfurt, the Limes which is the Roman Boundary lines that stretch about 550km through Germany, or along the top of the Rhine gorge.

How about Saxon/Bohemian Switzerland? With views like this, this, this, this, this, or this.

Hiking there is an adventure, because the trails can look like this, this, this, this, or this. Even teenagers love it there.

Here are the 5* Tripadvisor Reviews:
Saxon Switzerland National Park
Elbe Sandstone Mountains
Czech - Saxon Switzerland

A good base is Bad Schandau.
In case of bad weather you can see Prague, Dresden or Meissen. And many other sights in the area, like Königstein fortress, Weesenstein castle, Pillnitz palace, Pirna...

A lot of good suggestions already.

Website of German National Tourist Board offers also an overview with map which may help you:
http://www.germany.travel/en/leisure-and-recreation/hiking/hiking.html

I think you need to provide specifics for what type of hiking you are looking at. There are so many well marked trails in every corner across Germany. Marked trails are not just in Parks and such. You can hike with a pack from one location to another. There are hiking services that offer hiking without a pack that transport your luggage from location to location, while you hike. How strenuous? Mountains? Cross Country? A region in mind?
http://www.deutsche-jakobswege.de/wege-uebersicht.html

I really enjoyed Rugen, and I stayed in Sassnitz for some day hikes in Jasmund National Park. That said, because of the location, it may be too far from the other places you want to see in Germany.

You should also check with the Volksmarch clubs. Lots of nice walks thru places rarely visited.

Volksmarch info at dvv-wandern.de

Did a two day hike up to the top of the Zugspitze several years ago. It was great.