That would take a whole another post to answer fully, but allow me to take a brief stab at it. Alexander's empire was a strange fusion of Greek and Eastern influences. Generally, Macedonian generals appointed by Alexander would work with former Persian satraps over his new provinces. Alexander would leave a small contingent of Greek/Macedonian/ or Mercenary troops who would sometimes form a small colony (This became a common practice for the Ptolemies decades later). Interestingly enough, many of Alexander's Macedonian companions accused him of becoming "barbarian." In what some scholars call a pragmatic move, Alexander increasingly adopted eastern clothing and practices. Additionally, Alexander adopted eastern troops into his own companion cavalry (a huge offense among his Macedonian and Greek veteren troops).

A huge scandal at the time was Alexander's adoption of the Persian practice of proskynesis which essentially meant laying prostrate on the ground before the ruler. Macedonians who saw themselves somewhat equal even to their king, were appalled at this new practice, causing some to even mutiny against Alexander.

Overall, its difficult to assume how "eastern" or how "Greek" his empire would have been due to his early death, but we can determine which of the successor kingdoms were more Eastern (when I say Eastern I am referring to the old Persian empire practices).
Remember, when Alexander died, his empire broke among his top generals. Although still debatable, the Selucid empire was the most "Eastern" while the Antigonids in Greece and Macedon were the most "Macedonian or Greek." Hope this helps somewhat.