So, Greek architecture, one of the most influential architecture you can find find on the planet, but was it just local or did it have external influences which came from other cultures?
I'm no expert and I'm not qualified for giving a detailed response unfortunately, but you may want to look into Hittite architecture. Solely from my observations and a few lines from a history documentary on the Hittites, it seems Greeks were influenced to an important degree by the Hittites in many ways. For example, Zeus bears similar traits to the chief Hittite God Stormfather.
Unfortunately, in my searchings at least, there seems to be a scholarly road block when it comes to who influenced the Greeks because there seems to be a strong will to seperate them from the ancient near eastern cultural sphere in mainstream western historiography.