One in eight asylum seekers disappear after registration according to press reports. One way to get an idea where those that do not leave the country might be is to use google searches to trace them. Syrian refugees are the largest group. Whenever they get internet access they will definitely try to read news in Arabic about Syria (in arabic سوريا). There is admittedly a lot of noise and uncertainty to make precise estimates but you might get an idea by looking at these maps.
Obviously, with the exception of Berlin, Syrian refugees do not go to East Germany. Looking at cities we see that, with the exception of Neuhausen ob Eck in Baden-Württemberg, they go to large metropolitan areas in the West or Berlin (where they can obviously blend in easier).
What explains Neuhausen ob Eck? Most likely that refugees have better internet services in the shelters there? Not sure.