Why did Avraham return specifically to the same spot where he had stood the day before?
Seforno: He wanted to continue where he had left off yesterday - to plead for mercy, since he had been unable to find any merits on their behalf according to the Din.
Michtav me'Eliyahu (Vol. 5, p. 427): Avraham fixed a place for his prayer, and made himself a place for revelation of Kevod HaSh-m, so HaSh-m became his place. 1
Compare to Maharal (refer to 19:27:1.1:2).
"Avraham arose... to the place where he had stood before HaSh-m." The Gemara (Berachos 6b) derives from here that one should make a fixed place for prayer. Why is this so?
Maharal #1 (Nesivos Olam, Nesiv ha'Avodah Ch. 4, p. 86): Prayer is attachment to HaSh-m. A haphazard or chance encounter does not create a connection; this requires consistency.
Maharal #2 (ibid.): By making a fixed place, one shows that he wants a place with Hash-m. Avraham personified this trait (based on Tehilim 110). The world was created for Avraham's sake; 1 he was the root of all who came after him. A root must have a place, a source of nourishment to enable further growth.