Basically nothing, and we shouldn't necessarily expect to find them. Exactly how far Nebuchadnezzar made into Egypt is not clear. The inscription (apparently some kind of religious text) from Year 37 references heavy resistance by the Egyptians, which could suggest that they just didn't make it very far. All indications from the Babylonian record, Amasis' stele from Elephantine, and the Classical sources of Herodotus and Diodorus Siculus suggest that Nebuchadnezzar was trying to restore Pharaoh Apries to power, and possibly annex some border territory for Babylon. They probably wouldn't want to destroy the cities they did capture, just loot and pillage.

The only site we can really be sure of is Pelusium, right on the western edge of the Sinai Peninsula, which is further complicated because it was captured by the Persians just 40 years later and most of the archaeological work has focused on the higher, Roman layers. The Amasis Stele only specifies a failed battle to defend Bmw, identified with Herodotus' Momemphis, but we have no idea where that would be located. Further, if most of the conflict took place as pitched battles, there wouldn't be evidence for that either. All but the largest ancient battlefields tend to be archaeologically empty and all are difficult to find because they are just open space.

The only location mentioned in the Babylonian record is Putu-Iaman. Like Momemphis, we have no idea where this was, but it has been the subject of extensive debate. In Hebrew, Put, has typically been identified with Libya based on its translation in the Koine Greek Septuagint Bible. This has generally led translators to apply the same to other Semitic or Semitic influenced texts. In Assyrian inscriptions, variations of Iaman appear to be a form of "Ionia," the Greek cities on the western coast of modern Turkey. Variations of Ionian form the basis for many languages' exonyms for Greece to this day. Many scholars, such as T.C. Mitchell, have used these connections to interpret Putu-Iaman as "Greek Libya," meaning Cyrene. Depending on how you interpret the highly damaged Babylonian tablet, that could be understood to mean that Nebuchadnezzar went much further west into the Nile Delta and beyond.

However, there are problems with that interpretation. The total lack of any other reference to a Babylonian incursion into the central Mediterranean is a glaring example, and the fact that it would necessitate either a march over the desolate coast of eastern Libya or the longest Babylonian naval expedition on record in the face of Egyptian superiority at sea are another. It's much more likely that it refers to Cyreneans being brought to Egypt in support of Amasis, which doesn't help identify a location.

Even then, there is a further problem identifying Putu-Iaman as Cyrene. The Babylonian document refer to something in the next line as a "far lands among the sea," implying an island. The Stele also refers to Apries taking refuge on an island for two years after the invsion had failed. and the Hellenistic Egyptian historian Manetho refers to Apries taking refuge on island. Many sources from the Biblical Jeremiah and Ezekiel to a number of Classical Greek authors to the 8th Century CE Cambyses Romance identify this island as Tahpanhes, also known in Greek as Daphnae, a Greek outpost on an island in Lake Manzala. Ivan A. Ladynin^1 argues that this is the most probable identification for Putu-Iaman.

Admittedly, that doesn't clarify the use of "Putu," but it does mesh with all of the other available information. That would also locate all of the identifiable locations at the eastern edge of the Nile Delta, plausibly indicating that the invasion didn't press very far into Egypt to begin with.

1 https://istina.msu "dot" ru/media/publications/article/1e3/4f2/2758543/The_Elephantine_Stela_of_Amasis_Endl.pdf