He (Maimonades) and his family lived there during the supposed "Golden Age." Saying they "left" is cute. Why do you think they "left"? Actually his family was in hiding for ten or so years in Spain (Gee. Why were they hiding?) Then they escaped to Morocco where they continued to face persecution so the "left" there too. They did get to Egypt (via Palestine) as you suggest. There Maimonades was put on trial for his life for heresy and somehow escaped conviction, for which we are supposed to be grateful. I suggest to you contrast the treatment Maimonades received from the Muslims with the treatment Rashi (another great Jewish scholar) received from the Christians in France where he lived at about the same time. (Rashi made wine.)
ML/NJ