Where did Moshe go?
Ramban #1: After the people returned to their places, Moshe went to honor them - to take leave of them before his death. 1
Ramban #2 (on Pasuk 24, citing the Ibn Ezra): He went to bless the people - Parshas Vezos ha'Berachah, which was actually said here. 2
Seforno: What the Pasuk means is that he went and spoke to the people to comfort them over his forthcoming departure, 3 in order not to detract from the Simchah of the B'ris 4 that they had just entered into with Hashem.
Moshav Zekenim (citing Midrash Agadah) #1: Moshe went to the mountains, hills, seas and rivers to ask them to beseach Hashem to have mercy on him and extend his life. 5
Moshav Zekenim (citing Midrash Agadah) #2: Moshe went to each tribe, told them that he will die, and informed them that Yehoshua will distribute Eretz Yisrael (see Pasuk 7).
Targum Yonasan: He went to the Beis-ha'Midrash (the Ohel Mo'ed) 6 to teach them the rest of the Parshah and Parshas Ha'azinu. 7
Oznayim la'Torah: He went to ask the people whether they would accept Yehoshua as his successor, 8 which explains why he went to speak to them alone - without Yehoshua - rather than call the people to him, and why - in Pasuk 7 - he then called Yehoshua to appoint him as his successor. 9
Ramban: Like a person taking leave of his friend, who asks permission before departing.
Refer to 31:24:2:1*.
Seforno: Like "Vayeilech Ish mi'Beis Levi", in Shemos, 2:1.
Seforno: As in Tehilim, 149:2. See also above 27:7.
And when the Torah writes later - 32:44 - "Vayavo Moshe",it means that he returned.
See Na'ar Yonasan.
Like we find in connection with Betzalel. See Oznayim la'Torah DH 'Vayeilech Moshe' #1.
Oznayim la'Torah: See also Oznayim la'Torah, DH 'Vayeilech Moshe' #2.
Why does the Torah write here "Vayeilech", but not regarding other matters that Moshe told Yisrael?
Hadar Zekenim: Because up until now, Moshe gathered the people via the trumpets. But now, on the last day of his life, they were hidden
As the Pasuk writes in Koheles 8:8 "Ein Shilton be'Yom ha'Maves." Refer to Rashi in Pasuk 28.