My favorite acclimatization spot is Horseshoe Meadows.
(Google map) Elevation is 10,000' (3050 m).
The road is now open, and the campground will be open when you are here. I like to sleep here one night, then at the Whitney Portal walk-in sites (just below the trail head) the night before starting up the trail. If you can sleep at these higher elevations, your acclimatization gets well under way.
Seeing you are coming from Germany, I hope you are driving a car, as transportation in these places without a car depends on your thumb, which takes a long time sometimes. If you can bring just enough light camping gear (you don't need a tent!!), the two places I use are the best you can do.
Though you will probably run into snow,
Trail Peak is an easy hike out of Horseshoe Meadows. You can hike up the Main Mt Whitney Trail as far as Lone Pine Lake without a permit, too.
