Shaykh Bin Baz was asked:
Is there any reported Hadith to support that it is Mustahab (desirable) to change the place when performing the Sunnah Ba‘diyyah (supererogatory Prayer performed after an obligatory Prayer)?
I do not know of any Hadith Sahih (authentic Hadith) reported in this regard. However, Ibn ‘Umar (may Allah be pleased with them both) and many of the Salaf (righteous predecessors) used to do so. This is a matter open to choice, praise be to Allah! There is a Da‘if (weak) Hadith reported by Abu Dawud (may Allah be merciful to him) concerning it that is supported by the actual action of Ibn ‘Umar (may Allah be pleased with them both) and the Salaf. May Allah grant us success.
AbdulFattaah Bin Uthman