Al-Andalus was culturally, economically and socially very advanced for its time

Yes, this is correct. This is true also for Sicily.

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What about the neighboring Christian kingdoms of Iberia? Were they also more advanced than the rest of Western Europe as a result of contact with the Muslims?

I suppose that at least until year 1000, Byzantine Empire was the most advanced realm in western world, then overtaken by the mercantilistic Italian republics and "comuni", such as Florence, Genoa and Venice. Spain, on the other hand, even during its golden age, was importing knowledge from outside instead of producing it locally. For instance, Columbus and Amerigo Vespucci were Italian, Vasco da Gama and Magellan were Portuguese, El Greco was Greek. To make the situation worse, Spain expelled in 1492 the Muslims and the Jews, many of whom were doctors or merchants, and had a higher level of education than the catholic population. This facts, however, didn't prevent Spain from becoming the most powerful western kingdom during the XVI century, and to embellish cities like Seville with everlasting architecture and art treasures.

Or were they relatively backwards compared to places like modern-day Germany and France given their peripheral location within Christendom?

Only in the 17th century Germany, the Netherlands or France overtook Southern Europe (especially Italy, that was the wealthiest European place during the Middle Age and Renaissance). This was an effect of the new sea trades with America and Asia, the progression of the Turks in Eastern and Southern Mediterranean and the loss of centrality of Italy in trades schemes. Some historians say the Protestant Reformation may have had some effects. By that time, Al-Andalus was already totally disappeared, and it seems that development of trades and technologies played a mayor role in advancement of societies rather than centrality or peripherality within Christianity.