What was Yitzchak doing at the well of Lachai Ro'i?
Rashi: He went there to bring Hagar back to Avraham, to remarry her. 1
Seforno: He went to pray at the same spot where Hagar (his maidservant) had been answered. 2
Rashbam and Ramban: The well was situated in the south of Eretz Kena'an, which is where Yitzchak was currently living, as the continuation of the Pasuk indicates. 3
Ramban (citing Targum Onkelos); He came there from Be'er-Sheva (in the south), where Avraham and his family were currently living. And that is where he brought Rivkah after they met in the field.
Targum Yonasan: He actually came from the Beis-ha'Medrash of Shem, where he had been studying for three years since the Akeidah 4 - which was situated in the south in the vicinity of the well of Lachai Ro'i, by which Hashem, who sees but cannot be seen, revealed himself to Hagar.
Malbim: The well was in the south, between Kadesh and Bared (16:14), which is where Avraham went after Sedom was destroyed (20:1), and Yitzchak was living now. He used to go there every afternoon to meditate alone, and pray Minchah at the place where an angel appeared to Hagar.
Ha'Emek Davar: He was living in Be'er-Sheva with Avraham. Due to Hashgachah, he had gone to Be'er Lachai Ro'i, and Rivkah saw him and was awestruck at his appearance. Had she first come to Avraham's house and talked with him, she would not have been mesmerized when she saw Yitzchak, and would have conducted with him like any wife does with her husband. 5
Refer to 25:1:1. Oznayim la'Torah: We can learn from here that, after the death if their mother, children should not stop their father from remarrying (or their mother after the death of their father).
See also 16:7 and 20:1.
Ha'Emek Davar (65): Fear of him became fixed in her heart, and her entire life she could not argue with him, e.g. when she saw that Esav is tricking him. She was unlike Sarah and Rachel, who had occasion to speak boldly to Avraham and Yakov, respectively.