Reddit mentions of Decline and Fall of the Sasanian Empire: The Sasanian-Parthian Confederacy and the Arab Conquest of Iran (International Library of Iranian Studies)

I would recommend Sasanian Persia: The Rise and Fall of an Empire in a second. Also, how about these:

Shadows in the Desert: Ancient Persia at War, by Kaveh Farrokh:

https://www.amazon.com/Shadows-Desert-Ancient-General-Military/dp/1846031087/ref=sr_1_1?s=books&ie=UTF8&qid=1468190893&sr=1-1&keywords=Shadows+in+the+desert

Sasanian Iran (224-651 CE): Portrait of a Late Antique Empire, by
Touraj Daryaee

https://www.amazon.com/Sasanian-Iran-224-651-CE-Portrait/dp/1568591691/ref=pd_sim_14_2?ie=UTF8&dpID=51ADXBJ1MOL&dpSrc=sims&preST=_AC_UL320_SR212%2C320_&psc=1&refRID=4GCETN8G2E93J2M2SPBJ

Decline and Fall of the Sasanian Empire: The Sasanian-Parthian Confederacy and the Arab Conquest of Iran, by Parvaneh Pourshariati:

https://www.amazon.com/Decline-Fall-Sasanian-Empire-Sasanian-Parthian/dp/1845116453/ref=pd_sim_14_10?ie=UTF8&dpID=41ShWgvQD0L&dpSrc=sims&preST=_AC_UL160_SR104%2C160_&psc=1&refRID=N1AQCWRJ83JPEA7P925W

A historian recommended me these for the Sassanian Empire:

Sassanian Iran

Fall of the Sassanian empire - Expensive on amazon, here's the entire book online for free.

Unfortunately, there are some who are better suited to recommend some of the ancient works that you are looking for, but here are some for the classical/late antique period:

On Persia:
Parveneh Pourshariati's Decline and Fall of the Sasanian Empire was extremely important and full of new approaches to Persian history in the centuries immediately prior to Islam. It's not the easiest of reads from cover-cover, but if you are seriously interested, go here. It is especially useful for its discussions of some of the "minor" pre-Sasanian and Sasanian families and dynasties that made up Persia and its environs.

For a very similar period of Persian history is Touraj Daryaee's Sasanian Persia: The Rise and Fall of an Empire

On Syria:

Ross Burns' Damascus: A History is an extremely useful and extremely readable history of the capital of Syria as a case study of settlement in Syria over the millenia. The early sections of it I would highly recommend.

More generally:
Cyril Mango's The Oxford History of Byzantium is a useful, concise work on Byzantium.

It hasn't been mentioned here, but Peter Brown's World of Late Antiquity is also considered by a great many to be essential reading on the period, if you've never read it before. Plenty of people strongly disagree with it, but everyone who works on the ancient/late-antique world is forced to engage with it at some point, whether they like it or not. It is also extremely readable.

Hmmm well to me, in my readings (MA in archaeology, Sassanian landscapes, work as a edit: consultant archaeologist these days) that much of the intellectualism that the Caliphate is credited with is derived in fact from their converted East Roman/Sassanian bureaucrats, who while helping to administer this new empire continued on with the Eastern pursuit of science/religion/philosophy, without the successful integration of these people into the Caliphate (ie the Mongols, who slaughtered the entirety of Abbasid Baghdad, wiping out a great center of intellectualism) I doubt the Ummayads would have maintained an intellectual tradition, being the dour, hardy, barely literate desert warriors that they were at heart...they seemed to be far more interested in their palace/political worlds then their intellectual life...
see:

http://www.amazon.com/Decline-Fall-Sasanian-Empire-Sasanian-Parthian/dp/1845116453

http://www.sup.org/books/title/?id=3151