It was a mix of lots of different cultures, however primary spoken language was Greek.

Anatolia was Hellenized after the conquests of Alexander to some extent, but since having hosted countless ethnic groups for thousands of years it probably reflected great diversity even after hundreds of years of Greek rule. Hittites, Phrygians, Lycians etc. were assimilated at some point but Armenians, Kurds, Jews, Lazes, Assyrians and to some extent Georgians and Arabs existed in Anatolia in the eve of the advent of the Turks (most of these ethnic groups still survive in small communities in modern Turkey).

Byzantine towns in Anatolia reflected the presence of a strong central state, with a bureaucracy and clergy directly appointed and commanded from Constantinople. However they also reflected the ethnic diversity of local populations along with different commercial activities that greatly depended on their immediate surroundings (such as harbor towns, agricultural towns, etc.).

You should definitely take a look at "The Decline of Medieval Hellenism in Asia Minor and the Process of Islamization from the Eleventh through the Fifteenth Century" (1971) by Speros Vryonis for a much more detailed account of both the state of Anatolia before Turkish conquest and its subsequent Islamization.

It's a good question that is interesting and, as far as I know, not dealt with by its own history—people tend to cluster into Greek, Byzantine, or Turkish camps and do their research from there. The most famous Byzantine histories—Gibbon's and Norwich's—are laden with bias but can give you broad strokes; maybe better off using Vasiliev, Mango, and Treadgold but they're older now and probably have people annoyed with them.

In any case, your underlying question is "how can I get rid of my bias?" and the answer is to realize that you already know Anatolia was the home of Hatti (the Hittites) & Trojans, Lydians & Lycians, Phrygians, Georgians, Armenians, &c. &c. The Persians, Romans, and Greeks taxed them but mostly left them alone as long as they didn't revolt and (later on) held the orthodox faith (albeit the orthodox faith of the eastern half could go from Christianity to Zoroastrianism to Islam to Christianity again depending on how various border wars played out).

Most seem to have spoken some variety of Indo-European language and are usually presumed to have spread south from the plains north of the Caucasus in different waves during the 2nd millennium BC. By the Byzantine era, most were Hellenized (especially on the Aegean coast) but the Armenians, particularly, were their own group and at the time spread much further all through the eastern half of the peninsula. The Turks came as conquerors but (for what it's worth) some DNA genotyping bears out that large numbers of people in Anatolia are genetically whatever they were before (R1b): they just adapted to Islam and Turkish culture and got on with their farming.

One example of how thorny this can be is the fight over who, exactly, the medieval Abasgians were, which plays into whether their independence from Georgia should be accepted, ignored, or condemned.