Something representing autocephaly of Orthodox churches?
I don't think that relocation of holy city is good idea: don't think that Moscow can be called as the worldwide center of Orthodoxy anytime. All of this "Third Rome" thing was mostly for internal affairs, and authority of Constantinople, Jerusalem or another Ancient Patriarchate was never disputed. ROC counts as fifth in Ortodox ranks.
But additional shrines that steal Jerusalem money probably will be reasonable.
Why not to make this as a project?
"Translatio Imperii": needs Orthodoxy as state religion, available if all of Orthodox shrines are under control of non-Orthodox civilization and between, probably, Theology and Civil Liberties.
Effects: spawns "Seat of the Patriarchate" national wonder in capital: minor shrine, provides up to +10 gold to owner, excludes cities of owner from "major" shrine (that is still in Jerusalem).
So Byzantium will build it after loss of Jerusalem, and Moscow - after fall of Constantinople.
Some alt-historical possbitilies include first build by Rome/Egypt/Phoenicia (Orthodoxy founded not in conquered area, and this civ is alive in Medieval - nothing bad, just another Ancient Patriarchate will form Ecumenical Church) or HRE/France if Catholicism founded lately, but Russia will steal it nevertheless after they'll convert to Catholicism. And Third Rome in Addis-Abeba will be awesome too.
The reason why I am speaking about the new wonder abstractly is that both Saint Basil's Cathedral and the Kremlin could take this role. The Cathedral would be more fitting and my preference because it has a more overtly religious nature, on the other hand the Russian Orthodox patriarch actually resides in a Church in the Kremlin.
Kremlin, probably, is bad idea, can't think about it another than a strictly secular wonder.