That would depend upon what you are aiming to find.
- The Lomekwi site shows stone tools that around 3 million years old.
- Jericho is over 10 thousand years old.
- Gobekli Tepe is at least 11 thousand years old with some nearby sites being at least 12 thousand years old.
- The Cactus Hill site is at least 16 thousand years old.
- Tel al-Qaramel is at least 12 thousand years old.
- Theopetra is around 135 thousand years old.
Obviously, some of these are more important than others. Theopetra just shows that some people built a wall (most likely to block wind) at a cave entrance, while Qaramel shows people having built large burial mounds. Jericho and the various sites at and near Gobekli show people having built cities. Importantly, the flooding of low coastal areas during glacial melt explains the rather "sudden" appearance of complex construction at both Jericho and Gobekli (and slightly later Sumerian and Indus Valley) sites. People would have fled those now under water areas quickly, and they'd have taken the story of the flood and devastation with them along with their knowledge of construction. Accordingly, we have a flood myth in Semitic culture and a super old city. We do not know the myths and legends of Gobekli, but it doesn't make sense for "primitive" hunter gatherers to have suddenly invented construction, sculpture, city planning, logistics, and so on. It makes far more sense that they'd have fled an older site that was flooded by glacial melt.
