Is it part of the Sunnah for the deceased to be buried in the place where they died?

The default is to bury the deceased at the place of death, as was the practice of the Companions.

The majority of jurists disliked transporting the deceased before burial to another country unless there was a valid reason, such as preserving their sanctity from violation, or comforting their family and enabling them to visit, or transporting them to a better land hoping for blessings. They also stipulated, for the permissibility of transportation, that the deceased should not decompose due to the delay, and their sanctity should not be violated.

Ibn Hajar stated that the dislike or recommendation of transportation varies depending on the purpose. Prohibition applies if there is no preponderant reason, and recommendation applies if the transportation is to a virtuous place like Mecca.

Al-Mazari held the view that it is permissible to transport the deceased from one country to another, citing the burial of Sa'd ibn Abi Waqqas and Sa'id ibn Zayd in Medina after their deaths in Al-Aqiq.

In summary: The Sunnah is to bury the deceased at the place of death, and they should not be transported unless for a legitimate reason.