3 weeks in Germany

I am looking for less touristy places with great nature landscape. I am also looking to hiking from town to town

You can do this just about anywhere in the country, but I'll recommend two areas I know best.

One, Franconian Switzerland, is the triangular-shaped territory between Bamberg, Nürnberg and Bayreuth. Apparently, the rock formations and low mountains here reminded someone long ago of Switzerland, hence, the name. To me, it looks nothing like Swizterland at all, however, it's still very scenic. The region is filled with castles and small scenic towns, and it's a popular weekend getaway for camping and kayaking.

Two, the Odenwald, which is the mountainous region south of Frankfurt. Same deal, plenty of hiking, great small towns, interesting rock formations, castles, etc. And the Neckar river cuts through the southern portion of the mountain range, forming a deep valley that looks similar to the more famous Mittelrhein.

I like Tom's suggestions. I also like the Altmühl River Valley (Altmühltal,) also in Franconia but to the south.
http://www.dw.com/en/discovering-the-altm%C3%BChl-valley/a-1776689
Pappenheim:
http://www.treuchtlingen.de/fileadmin/media/Touristinfo/Blick_auf_Pappenheim_vom_Weinberg_aus-ch.link.jpg
http://www.pappenheim.de/Town-of-Pappenheim.22+M5d637b1e38d.0.html
Eichstätt:
https://www.nuernbergluftbild.de/images/luftbild/Q07050507d.JPG
Panoramaweg trail: http://international.naturpark-altmuehltal.de/en/topten/altmuehltalpanoramaweg/ (click on Further Information on right to see walking segments and towns connected.)

Since you mention hiking and great nature landscape as preferences, I would suggest looking at a couple of Cicerone guides for areas that make sense for a Munich to Frankfurt itinerary:

Walking in the Bavarian Alps: 85 Mountain Walks and Treks

Hiking and Biking in the Black Forest (much more about hiking than biking)

"...and my research is going nowhere." Why? Which books are you using? You have just under 3 weeks. Do you want to stay in between Frankfurt and Munich, or do you want go somewhere very different, say the Berlin area, or up north to Schleswig-Holstein, or to the Baltic area? I would suggest Schleswig-Holstein.

Maybe one of the Jakobswege.

http://www.deutsche-jakobswege.de/wege-uebersicht.html

The Northern part of the Oberpfälz and adjoining Fanken area is pretty rural and non touristic.

You could Wander the Fichtelgebirge:
http://www.bayern-fichtelgebirge.de/index2.htm
http://www.fichtelgebirge.net/sport-freizeit/wanderwege

There is the Oberpfälzer Wald Zoigl Beer Region too. The dialects are really heavy and far away from Hochdeutsch, but with the American training area near you'll get by:
http://www.oberpfaelzerwald.de/data/mediadb/cms_mime/%7B4c1195c4-7364-7167-0972-5f4258aa3663%7D.pdf