Hi,
I´m Spanish, not German, but being it at 6 Cessna flight hours from my home airport and having flown it a couple of times, I hope I can help in some way.
There is GA in Germany, don´t worry. They are, with France and the UK the most "Cessna populated" countries in Europe. You´ll find plenty of grass strips, airports... lots of airfields scattered all around. The problem is, or better, the problems are:
-If there´s a grass strip there´s a Dangerous airspace right South East to it, an international airport right North, an Aif Force base right South West, so you have a narrow VFR corridor to get out that mess.
-It´s WAY TOO EXPENSIVE. All the data Ed provided are quite accurate, leaving you with a final total price of some $200 per hour on a regular 172 (the plane itself, the landing fees, the...).
-It´s possible for you finding a N- airplane there, but it will be a hard job. This leads us to the next point.
-Next point: You´ll need to get a JAA license. Converting a FAA license into a JAA license consists, more or less, in joinning a school, writting the tests and the check ride. The total cost of this can be pretty high because you´ll be need to fly some dual, and with these prices...
Anyhow, there are flying clubs. Every country has its own National Flying Club and, be sure, most of that airfields will have one. No idea about Stuttgart itself, but check around it. On my flights I´ve seen billions of airports, not to mention the grassfields with some Robin or Rallye down there.
My two cents.
