Do you speak Greek? Because in Greek Nicaea is always spelled with a Greek letter that looks like our K, Νίκαιας.
I just looked it up in my dictionary and it says nee-KEH-ah, for both Nikaia and Nicaea, which is also spelled Nikea and seems to be the same name.
I bet Nice-ee-a is an English pronunciation as it doesn't sound Greek to me at all. Do you have a source where you got your information from? Just interested.