Get yourself a Simson S51 if you can. They are very popular, a little bit of ost kultur that seems to have spread. I've been wanting one since I saw a green one on my last visit. I know they are popular with teenagers because of the way the law works.
There are quite a few pretty active people on instagram who work on mopeds/mofas I'd suggest maybe contacting them. Off the top of my head I can think of one called Clarkes67 on who catalogs German vintage vehicles from the East, he might be a good start to get you in contact with people. How long are you staying?