I would try Peter Adamson's history of philosophy podcast/books.(I should probably watch/read those one day).

I definitely agree that Nasr's introduction is well worth reading. The subtitle, as Brian says, is philosophy in the land of prophecy, and Nasr goes out of his way to remedy rationalistic misunderstandings of Islamic philosophy and thought, emphasising the Islamic nature (its insistence on the oneness of God, its concern with being or Wujud) and creativity of Islamic philosophy. He also tries to correct the common Western misunderstanding that Islamic philosophy came to an end with Ibn Rushd (Averroes) or that Islamic thought is more or les synonymous with the voluntarism of Asharite Kalam. Often you would never even hear of the likes of Mulla Sadra in older Western histories of Islamic philosophy. Nasr is keen to show that, especially in Persia, the Islamic philosophical tradition continued until this day as a living tradition blending philosophy, gnosis, and faith, and that even some of its greatest practitioners lived long after Ibn Rushd. Even the Islamic Peripatetic school was revived by Al-Tusi and others in the thirteenth century. He also explores schools of Shi'ite thought and philosophy, such including the transcendent philosophy of Mulla Sadra and Ismaili thought.

Better?

I believe that it is better, at least when it comes to peripatetic (which is somewhat of a misnomer, seeing as they blend Platonism and Aristotelianism). There was less philosophy proper - called falsafah and later hikmat​ and in distinction to either Kalam or Sufi gnosis - in these lands after the twelfth century (although it is didn't die out completely). The Kalam itself, that in some ways was, in its Asharite variety, was always opposed to philosophy, became more philosophic. Harry Wolfson's work The Philosophy of Kalam is a good introduction to this latter discipline (though, contrary to the Amazon blurb, Kalam, though it became more philosophised, is not the nearest Islamic equivalent to what we in the West call philosophy, it is much closer to what we consider theology, though Islamic philosophy itself came to deal more and more with what we consider strictly theological issues whilst the Kalam became more philosophised).