Wikipedia articles on the "History of Geodesy", "Earth's circumference", and so on give a thorough summary of potential candidates, but suggest that this question isn't going to be answered decisively without a major discovery of new evidence.
Henry's answer raises the main problem: ancient units are imprecise. Arab astronomers under the Caliph al-Ma'mun confronted this problem by making their own measurements (c. 820 AD) which were very possibly more precise than the Greek ones. But in making this comparison, we confront the same problem again. Just as they didn't know enough about Greek stadia to rely on earlier measurements, we don't know precisely enough how long their cubits and Arabic miles were to say with confidence what they found.
When we get to early modern Europe, then there are clear and decisive breakthroughs. New instruments like the telescope and advances in trigonometry solved the fundamental problem. Jean Picard (c. 1670) is widely credited with making the first modern arc measurement.
Here we run into the further complexity that there simply is no single precise number even today. Sir Isaac Newton correctly predicted that the earth is an oblate spheroid, not a perfect sphere, as confirmed by measurements made in the 1730s. The equatorial circumference is about 40 miles longer than the meridional circumference (that is, through the north and south poles).