In the 3rd C Crisis eastern Empire option where would the capital be? Byzantium doesnt seem large enough just yet...
Perhaps Pella/Thessalonica? Athens? Antioch?
I doubt it would be Alexandria since Egypt is too essential for grain supplies to base the entire bureaucracy there safely.
It would depend on the needs and preferences of the people in charge during the... upheaval. Antioch may be too vulnerable to Persia. I agree Alexandria isn't the likely option. Athens might work, from a position of historical prestige. It's also possible that an alt-Constintinople just gets founded (maybe in roughly the same place, maybe somewhere else) at a 'new' location that is deemed best.
Ephesus perhaps? Or again Pella? Both of these have most of the strategic advantages of Byzantium and are much better established c 270 CE