Geographical centrality is not really the most important feature of a capital, and certainly not important enough to overwhelm others to the extent that a small and isolated archipelago somehow becomes attractive.
Most of the world's capitals aren't really anywhere near the georgraphic "centre" of their nation - Washington D.C and Moscow are close to the eastern/western edge of their respective countries. New Delhi and Beijing are far off to the north of their countries whilst London is off to the very south-eastern part of Britain.
More important than centrality is proximity to major population and economic centres, which in the case of a surviving Roman Empire would very definitely be in Europe short of anything absolutely catastrophic or a much smaller empire. You would need the American provinces to have a far, far higher economic and demographic weight that the European ones rather than the rough parity they have now, and that would be challenging given that a united and continuing empire for all those millennial has the expected impact of more positive demographic trends in Europe (less destruction and fighting between nations) and more negative ones for America (fewer large waves of immigration early on triggered by one conflict or another).
Of course, if you do want to go for the catastrophic or smaller empire route, far more opens up. A rump Italian/North African state would be an interesting colonial competitor to other states based on the Atlantic seaboard, and could ostensibly (via ports based in OTL morocco which would be fairly favourable to colonial development) develop a large enough overseas empire and sustains it long enough that it becomes desirable to transfer administration there.
Or you can just nuke everything in Europe. Nukes have this funny way of flattening alternate history implausibilities.
Most of the world's capitals aren't really anywhere near the georgraphic "centre" of their nation - Washington D.C and Moscow are close to the eastern/western edge of their respective countries. New Delhi and Beijing are far off to the north of their countries whilst London is off to the very south-eastern part of Britain.
More important than centrality is proximity to major population and economic centres, which in the case of a surviving Roman Empire would very definitely be in Europe short of anything absolutely catastrophic or a much smaller empire. You would need the American provinces to have a far, far higher economic and demographic weight that the European ones rather than the rough parity they have now, and that would be challenging given that a united and continuing empire for all those millennial has the expected impact of more positive demographic trends in Europe (less destruction and fighting between nations) and more negative ones for America (fewer large waves of immigration early on triggered by one conflict or another).
Of course, if you do want to go for the catastrophic or smaller empire route, far more opens up. A rump Italian/North African state would be an interesting colonial competitor to other states based on the Atlantic seaboard, and could ostensibly (via ports based in OTL morocco which would be fairly favourable to colonial development) develop a large enough overseas empire and sustains it long enough that it becomes desirable to transfer administration there.
Or you can just nuke everything in Europe. Nukes have this funny way of flattening alternate history implausibilities.