ثُمَّ يَصُومُ سَبْعَةَ أَيَّامٍ إِذَا رَجَعَ إِلَى أَهْلِهِ، وَإِنْ صَامَهَا بِمَكَّةَ بَعْدَ فَرَاغِهِ مِنَ الْحَجِّ جَازَ
Translation: Then he fasts seven days upon returning to his family; if he fasts those seven in Makkah after completing Hajj, that is also valid.
The final seven fasts have a different timing condition from the initial three. Al-Quduri explicitly permits them in Makkah after Hajj is completed. Thus return to one's hometown is not the only valid geographical setting, once the Hajj has finished.