Many surviving classical temples and palaces in the Levant and Asia appear to have been built by the Romans. Are there any notable ones that still survive today that where built specifically during the reign of the Seleucid kings (312 BC- 63BC)?
The Seleucids ruled over several very different peoples with different cultures, so strictly speaking there is no such thing as "Art and Architecture of the Seleucid empire". There is Hellenistic art but it was common to all Hellenistic states. There is Iranian (Parthian) art of the time when this part of the world was ruled by the Seleucids, and there is Armenian art of that epoch, etc.
Some of the finest Greek (Hellenistic) arts is connected with the Seleucid empire. The ruins of Pergamon and the Pergamon Altar. The dating is not exact, and I cannot say exactly whether Pergamon was under the jurisdiction of the empire at the time when the altar was created, the boundaries were fluid at that time.
Venus of Milo is another famous example. It is the work of Alexandros of Antioch (wee Wikipedia). Antioch was one of the principal cities of the empire founded by Seleucus I Nicator himself. But the place where the statue was found, the island of Milos, was not a part of the empire. Either Alexandros was a traveling sculptor, or it was purchased somewhere and then delivered to Milos.
The city of Hatra was probably built at the time of the Seleucid empire: https://en.wikipedia.org/wiki/Hatra#History but Wikipedia says it was destroyed by ISIL.