I don't see how bug-dating can establish anything unless that species of bug is known to have gone extinct at a specific point. How that extinction event took place would also be relevant, as its dating may have been established via carbon dating. So that does sound like it either is, or would be dependant on, carbon dating.
How to establish a non carbon-dated site as the oldest would have to be by historical and archeaological means, such as pottery and implements found, that would need to be correlated to historic timelines.
Our historical timeline was established by the Greek historians. We have a continuous narrative from about the archaic period of Greece through Rome to our times, to which we had to mix and match other peoples' narratives to build it back in time, jigsaw puzzle like, into the past from this point. The Jewish, Egyptian, Akkadian, Hittite, etc. narratives slip on by looking for common events reported by both, or datable things like eclipses or astronomical phenomena.
So Egyptian history is connected by a rising of the star Sothis, and an equating of Biblical Shisaq with Shesonq II, with the Jewish narrative connected via Josephus and the biblical narrative being paralleled by Greek Historians.
Once we established that, then the discovery of similar pottery and such in two sites, suggests that they were active at the same time: thus the latter site can also be dated, if we had by historic means established the first one. Egypt is an important lynchpin here, as its trade allowed us to establish rough timelines for many contemporary people like the Minoans, and thus add further timelines like the Neo-Sumerian lists onto our jigsaw puzzle. Carbon dating has been an important tool to support such efforts, but much of it was done long before it.
So to answer the question: I would opt for Eridu. Later periods of Egyptian history can be correlated with the Akkadian, which descended from the Sumerian. The Sumerians said that "the Kingship first descended on Eridu", and considered it their first city.
By archeological means and Sumerian tradition, a good argument for 3000 BC at least, could be made for it. By alternate dating, a sizeable settlement here can be pushed back beyond 5000 BC, though.