Well, I know that applies to some countries but not all. So just check up once again if your degree is recognized. If it is, that makes it that much less complicated.
Regarding universities good for training, I mentioned this in other posts but non-German medical graduates usually can't get into university hospitals (which in general are the best barring their location in big cities) unless they have an impressive CV (research, highly proficient in German, clinical attachments with doctors, neurosurgeons in this case, in Germany, and even contacts.)
Most non-German medical students usually get into rural hospitals/clinics/rehabilitations centers/nursing homes. The problem with this is that it can take longer to finish training programs (especially surgical ones) as you have to go to different hospitals to do procedures (because you won't be able to do all procedures in one small rural hospital just because they don't get many cases), which is a requirement to sit the Facharztprufung (specialty training final exam.)
So essentially, non-German medical graduates don't really get a choice of hospitals for specialty training. One just takes what one gets.