One highlight is the Middle Rhine valley, a UNESCO World Heritage Site.

http://en.wikipedia.org/wiki/Middle_Rhine

http://www.welterbe-mittelrheintal.de/

It is a picturesque region, has good wines and is crossed by the famous Rheinsteig hiking trail.

http://www.rheinsteig.de/

You can choose either Koblenz or Mainz/Wiesbaden as a starting point to visit that region. From there you have good train connections. See: http://reiseauskunft.bahn.de/ . If you have enough time, you can conveniently combine the Middle Rhine Valley with a visit to one of these cities.

The Moselle (Mosel) valley is nice too. It is different from the Middle Rhine valley, but has the same assets: picturesque landscapes and towns, good wine, hiking trails. Public transport is convenient too. And it is just a stone’s throw from the Hahn airport:

http://en.wikipedia.org/wiki/Moselle_%28river%29

http://www.mosel.de/

The Moselle valley can be combined with a trip to Luxembourg and Trier.

If you choose Luxembourg and Trier, why not add to Metz and Saarbrücken, to make it complete?

http://www.quattropole.org/en/home

Public transport between the four cities is straightforward. In Luxembourg, you can buy a ticket for public transport in the three countries:

http://www.cfl.lu/CFLInternet/Espaces/01EspaceVoyageurs/03TitresEtTarifs/03TarifsGrandeRegion/SaarLorLuxTicketunbilletpourtroispays.htm
 

If you are prepared to travel two hours by coach, you can also consider a visit to Heidelberg:

http://en.wikipedia.org/wiki/Heidelberg