Justinian's reign in considered a prime period of Byzantine Empire, and I always wondered why it's not considered a part of Ancient Roman period of the Empire. A lot of things were in line with ancient and late antiquity Rome: Latin is still spoken, large scale projects like Hagia Sophia happen, Eastern Empire's territory is intact.
Without actually going into the naming debate, were there really big changes in the Eastern Empire for the last 150 years before Justinian? What were the main changes in daily life, culture, administration, religion etc?
You bet your ass there were really big changes going between Theodosius and Justinian, especially on the administrative level.
Local town councils lost their importance and became mainly symbolic with little to no actual power. John Liebeschuetz has covered the reasons for their diminished importance extensively in The Decline and Fall of the Roman City. In essence, they really lost their ability to extract taxes fairly and they sometimes formed their own social circles to hoard their own wealth and punish their competition by forcing them to repay their debts immediately. Town councilors used to be responsible for the collection of taxes in the community, forgiving debts, etc., but they were replaced by other imperial representatives and special figures within the community like a holy man.
The provincial governors also became so corrupt and abused their power to such an extent that in some provinces such as Egypt, Justinian just outright stripped them of their judicial and financial obligations. Justinian actually put the dux completely of the civilian administration in Egypt. The duces (plural of dux) gained enormous administrative powers throughout the Eastern empire under Justinian because the provincial governors were so messed up. All this is covered in AHM Jones' The Later Roman Empire: A social economic and administrative survey <---- Definitely worth a read if you got time.
And really the culture of pilgrimage started taking off in the late fourth century, peaking in the fifth or sixth. The monastic style of a wandering pilgrim seemed to appeal to a lot of people. The state began to fund the construction of hostels, inns, churches, etc. to accommodate the increased traffic in the Holy Lands. Late Antique Travel into the Holy Lands is a pretty hot topic right now, but you should always start with Edward Hunt's Holy Land Pilgrimage in the Later Roman Empire.
Hunt, Edward David. Holy land pilgrimage in the later Roman empire AD 312-460. Oxford: Clarendon Press, 1982.
Jones, A. H. M. The Later Roman Empire, 284-602: A Social Economic and Administrative Survey. I-III. Oxford: Blackwell, 1964.
Liebeschuetz, John Hugo Wolfgang Gideon. The decline and fall of the Roman city. Oxford: Oxford University Press, 2003.