There's a lot of iron and steel just lying around in any plausible post-apocalyptic world. The entire Iron Age (including the Roman era) produced less iron than can be found in a single modern Panamax container ship.
The lowest plausible level of technology in such a world, assuming a large enough number of survivors to form a viable population at all, is roughly medieval - steel and iron tools, timber framed buildings, little or no window glass, handmade textiles, mostly agrarian communities with scattered small towns where produce can be traded. Animal drawn transport, with riverine and coastal transport by sail or animal drawn barges.
A big fall from today's OECD lifestyle, for sure; But a big step up from the Neolithic, which itself was a considerable step up from the Palaeolithic.