I saw that /u/Gankom mentioned this post in the Sunday Digest and I think I can tell you somethings about this. So sorry for this late reply /u/byzantine_meme but better late than never I guess.

Cordoba before the Umayyad dynasty

The city of Cordoba dates back to at least the Roman period. It's most defining features were the city walls that enclosed 78 hectares of the city and the bridge over the Guadalquivir. Both of these date back to the Roman period with the walls being comissioned by emperor Augustus. These walls and the bridge would in later periods be frequently renovated. After the fall of the Western Roman Empire this area came under the control of the Visigothic kingdom who had their 'capital' to the north in Toledo. During the later Roman and Visigothic periods Cordoban city life declined and at the end of this period most of the Roman city grid patern had dissappeared and the public Roman buildings had been abandoned. Despite this decline Cordoba was still one of the bigger cities and it was an important goal for the Muslim conquerors under Tariq Ibn Ziyad. About the early period not a whole lot is known and even the Islamic sources are from centuries later. There are different stories but apparantly Cordoba surrendered to the Muslims with a treaty so that they would still have a church in the city. The Visigoths had mostly focussed on the south west of the city with the basilica of Saint Vincent and the governors palace being located in that part of the city. The Muslims didn't change much and it appears they began to rule from Cordoba a few years after the initial landing from Tariq in 711.

Cordoba under the Umayyad dynasty

After Abd al-Rahman moved in in 756, things did change. He expanded the area of the old Visigothic palace/stronghold into a new palace and he converted the basilica of St. Vincent into a mosque after paying the Christians to move to churches outside of the city walls. This meant that the city within the walls was mostly reserved for muslims. There were still some christians and Jews inside the city walls with the Jews living in the north of the city as the gate there was called the Jewish gate. Cordoba from this period is often portrayed as this multicultural city where everyone lived together hapilly and this is somewhat of an exageration. Cordoba during this period would grow massively and although the estimates vary wildly a population of 300.000 seems the most likely which would make it the biggest city in Europe after Constantinople. Even in the Islamic world Cordoba was well known as a grand city. It was most famous for being an intellectual center. It is said to have had a huge collection of books in as many as seventy libraries throughout the city. It was a center of learning that would rival the house of wisdom in Bagdad. It produced many great scholars on a variety of subjects: al Ta'rikhi and Ibn 'Abd Rabbihi produced great works of literature and history and Abu 'I-Qasim al-Zahrawi of Cordoba (Abulcasis) was one of the great surgeons of the medieval era. It was however not all great as sometimes more 'pious' rulers would disapprove. Under al-Mansur there were book burnings of on some of the ancient greek works on logic and astronomy. The city's mosque was where most of the scholars were and it was expanded several times in this period to fit the expanding population. The city was also a center of manufactering with vast amounts of weavers, leatherworkers and it also had a big metalworking center. In the early Umayyad period the tollerance for other faiths was also remarkably high with christians and Jews even climbing to administrative functions. For example Hasday b. Shaprut was a Jew who was sent as a diplomat to the Spanish christian kingdoms to the north and who is also one of our few sources on the Jewish Khazars in what is now southern Russia. Another was Ibrahim b. Yaqub who went all the way to the court of Otto I of Holy Roman Empire. Things wouldn't go so well after the year 1000 of the christian calander. There was a berber revolt in 1013 that sacked the city and in this tumultuous period the Umayyads Caliphate would fall for good in 1031.

Cordoba in the post Umayyad period

Cordoba became first a republic ruled by three members of the same family consecutively (Jahwarid). In 1070 they were conquered by the Abbadids of Seville and in 1091 the city was taken over by the Almoravids. In 1172 the Almohads took over and they were a very repressive and puritanical regime. This was a period of roughly 150 years in which al-Andalus wasn't doing so great and the reconquista was picking up steam. In this period Cordoba was no longer a city of military of political importance. But the city's intellectual community did continue and produced some of it's finest scholars. Ibn Rushd (Averroes) the philosopher and physician is from this 12th century. Although the Almohads would eventually forcibly convert the Jews of Cordoba, before that some of the most famous Andalusian Jews lived in the city. Moses Maimonides, a rabbi, philosopher, diplomat and physician who went on to work for Saladin in Egypt. And other Jewish intellectuals also found their way to the courts of Castille and Aragon. The last of the Almohads died in 1233, afterwards the city fell victim to party strife and in 1236 it was conquered by Ferdinand III of Leon and Castille. Granada would become the most prominent Muslim city in al-Andalus as it would take in many of the people fleeing from conquered cities like Seville and Cordoba. Cordoba would again be an important military city but now it was for the Christians who used it as a base to launch their campaigns against the Emirate of Granada. The great mosque of Granada was now converted back to chruch and they pretty much build a church in the middle of the mosque (which looks hideous in my opinion).

To come back to your original question. No, Cordoba wasn't really all that prominent and was overshadowed by places like Seville and later Cordoba Granada although it did still have a thriving intellectual community untill the Almohads started calling the shots.

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Sources:

Robert Hillenbrand, ‘“The Ornament of the World” Medieval Córdoba as a Cultural Centre’, in: Salma Jayyusi ed., The Legacy of Muslim Spain (1994) 112–135.

Ann Christys, ‘The Meaning of Topography in Umayyad Córdoba’, in: Caroline Goodson, Anne Lester and Carol Symes ed., Cities, Texts and Social Networks , 400-1500. Experiences and Perceptions of Medieval Urban Space (2010) 103-123.