If you all don't mind me systemizing this a little bit, it would seem that the chances of Roman noble families surviving would have been highest where power was still exercized by Romans or at least in the name of the Roman state. Obviously, that means the Byzantine Empire, although even there the periodic rise of military dynasties meant an influx of provincial nobility, often from the frontiers, whose Roman heritage isn't all that clear to me. In Western Europe, southern Italy and the later Papal territories would be obvious candidates, as already said. As for the Germanic kingdoms, the chances of Romans making it into the secular elites were probably low. Thanks all for the discussion on Visigothic Spain - but how about the Banu Qasi? They were supposedly descended from a count Cassius who converted to Islam shortly after the Arab invasion. The account may be legendary but I'd like to hear the experts on it.
Also, wouldn't post-Roman Britain also be a good candidate? Power might have reverted to Celtic tribal leaders but presumably they would have been somewhat romanized in the 300+ years that Rome ruled there and have been accorded the status of nobility by the Romans. (I guess this goes to a definitional question. Are we counting only families that originated in Rome? All Senatorial families, including romanized Gauls? All local nobility whose claim to status was recognized by the Empire?)
Also, wouldn't post-Roman Britain also be a good candidate? Power might have reverted to Celtic tribal leaders but presumably they would have been somewhat romanized in the 300+ years that Rome ruled there and have been accorded the status of nobility by the Romans. (I guess this goes to a definitional question. Are we counting only families that originated in Rome? All Senatorial families, including romanized Gauls? All local nobility whose claim to status was recognized by the Empire?)