Any civilization leaves an imprint on an area it has colonized. Ancient Greece is no exception, and Greek colonization had a number of effects on the Mediterranean and Black Sea regions.
First of all, you might want to point out architectural influences. Having been settled or occupied by the Greeks, many regions started following the Greek style of architecture. For example, houses and temples were built like houses and temples in Greece would have been built. You can see that near Selçuk, for example, which is a town located in modern-day Turkey. Just outside, you can see the ruins of the ancient city of Ephesus, one of the oldest Greek settlements in the region. If you travel there, you can visit the ruins of buildings that clearly followed the ancient Greek architectural style.
Another influence of Greek colonization you might want to mention is religion. When they colonized various parts of the Mediterranean and Black Sea regions, the Greeks brought their polytheistic religion with them. They believed in anthropomorphic gods who resembled humans in their actions and physical features. In order to worship these gods, the Greeks built temples in many areas that they had colonized, and many local people at the time took on the faith of the Greek occupiers. This is why you can still see many ruins of Greek temples outside of Greece today.