"The Second World War was fought in Southern Europe too." And WWI as well. One of the most interesting memorials I've ever visited was located high in Italy's Ortler Alps, above the ski resort of Passo del Tonale. What is now a ski field was once the front line between Italy and Austria-Hungary. The memorial is carved directly into the rock, and nearby, you can visit a small museum that I think was called something like "The sounds of war". It occupies a shelter-cave, drilled into the mountain side during the war, and it allows you to experience what the war must have sounded like reverburating through the rocks. Kind of creepy. You can visit all of this by either attempting an extrememy difficult up-hill hike, or just ride the ski gondola.
Congrats on the Stuttgart assignment! You'll love it! Stuttgart isn't the prettiest city in Germany, but there's a lot to do, both in town itself and in the surrounding region. And if you like to ski, you're only about 2 hours away from Alpine resorts.
"Second, I would like to make sure we see World War sites, more specifically WW2." These are rather rare in Germany, for the obvious reason that the country wants to limit the opportunities for the tiny far right movments to memorialize the Nazis. But, you'll see a small, understated memorial in just about every town, which lists the war dead. When you see how many names are on some of these monuments compared to the size of the town, it becomes quite sobering.
One large, completely undamaged building project from the Third Reich era that is relatively close to Stuttgart is Heidelberg's Thingstätte. These were built on the model of an outdoor Greek ampitheater with the intention of using them for night-time propaganda rallies. The concept never proved particularly popular, but the Heidelberg's specimen remains completely intact, perfect acoustics and all, with the exception that the post-war government removed all the symbols associated with the Nazi era. It sits near the top of the Heiligenberg, the mountain on the opposite side of the river from the famous Schloss. You can either hike up or drive, although the road that leads up to the parking area is a little hard to find.
"The first question is since we have a car and an international license which places are better for car and which ones are better just taking the train." Traveling to any large city in Germany, train is usually more convenient. For exploring the regions outside of cities, a car makes things easier. For the most part, I don't find driving within German cities particularly difficult, with Munich being a huge exception. And unfortunately, the Stuttgart region has some of the worst traffic in Germany. You will hear the word "Stau" very frequently. Berlin has some awful traffic outside of the city, but I found the city itself surprisingly easy to navigate by car (although I only drove to and from my hotel). In general, cars are often more of a hastle than a benefit in most European cities. Even when I do drive to a city, I usually keep my car parked in a garage for the duration of the stay.