Paper-making and the printing press, so that whatever knowledge survived could continue to be passed on. Undoubtedly there would be significant local evolution of language if we lose electronic mass communication, so it will be essential to preserve the use of Latin as a stable language across space and time, giving us access to the Bible and the classics as well as the ability to write a letter to a neighboring kingdom. Hopefully, literacy would enable our children to receive and apply knowledge of the virtues of prudence, temperance, fortitude and justice, faith, hope, and charity.

Other than that, we'll need knowledge of food production, food preservation, as well as tool creation (i.e. blacksmithing) and construction based on locally available materials. The only tricky thing here is the "locally available materials" issue. I live in the desert. Would I be able to grow enough food on my land here if the city water were shut off?