Gemara

31b (Rav Safra): A Yevamah goes to the Yavam to do Chalitzah.

(R. Ami): She must go even from Tiverya to Tzipori.

(Rav Kahana): He learns from "v'Kor'u Lo Ziknei Iro (of his city)", not the Zekenim of her city.

49b (Mishnah): The Mitzvah of Chalitzah: the Yevamah and Yavam come in front of Beis Din. They give to him a proper counsel - "v'Kor'u Lo Ziknei Iro."

Yevamos 101b (Beraisa): "They will speak to him" - they give him good counsel. If he is young and she is old, or vice-versa, they tell him not to do Yibum. Rather, he should marry someone his own age and not bring quarrels into his home.

Rishonim

The Rif and Rosh (10a and 3:41) bring the Gemara on 31b.

Nimukei Yosef (DH Afilu): She must go even from Tiverya to Tzipori, i.e. even though the Beis Din in Tiverya has a greater Yeshiva and is more esteemed than the Beis Din in Tizpori. The Ro'oh says that she must go only if he is in Tzipori. If he went elsewhere, she does not follow him. Rather, we force him to go to her. "The elders of his city" applies only when he lives there. Also the Yerushalmi connotes like this.

Maharival (1:13): Granted, we do not find Poskim who argue with the Ro'oh. However, the Poskim wrote Stam that she goes to his city, i.e. in every case! It seems that they disagree with the Ro'oh. Or, since the Ro'oh taught a law based on logic, perhaps they all agree. It is a Safek. We cannot force the Yavam. Tosfos (Kidushin 60b DH Aval) says that if an Amora Ploni is unlike one Tana, and there are two ways to explain another Tana, Ploni can say 'I know that the true Perush is like me.' The Yavam can say 'I know that the other Poskim argue with the Ro'oh.' If he was Mekadesh another woman, Stam, he can force her to live in his place. If he stipulated not to move her, her place will become his fixed residence, but only after the Nisu'in. It seems that his city must have an expert Beis Din. We said that she must go even from Tiverya to Tzipori, i.e. even though Tiverya's Beis Din is greater. Had it said Stam, we would explain that this is whenever his city has a Beis Din that knows how to perform Chalitzah. Rather, it taught about Tzipori to teach that it must be expert to give to him good counsel.

Rambam (Hilchos Yibum 4:1): The Yevamah goes to the place of the Yavam and comes to the judges. They call to him and give to him a counsel proper for him and her. If it is good to do Yibum, they tell him to do Yibum. If not, e.g. she is young and he is old or vice-versa, they tell him to do Chalitzah.

Question (Mishneh l'Melech): When there is no expert Beis Din in his city, he goes to her city. What is the law if there is an expert Beis Din near his city?

Answer (Maharam Galanti 67): If there is no expert Beis Din in the Yavam's city, but there is one nearby, if there is an expert Beis Din in the Yevamah's city, the Ro'oh ruled that he must go to her city.

Radvaz (1:269): The Poskim bring Stam that she must go to his city. This is even if she is in Eretz Yisrael and he is in Chutz la'Aretz. Normally, one must pursue a good Beis Din - "Tzedek Tzedek Tirdof." It is a Gezeras ha'Kasuv that for Chalitzah we go to his city, even if there the Beis Din is inferior. Even though one cannot force his wife to leave Eretz Yisrael, rather, (if he wants to leave) he must divorce her and pay her Kesuvah, we do not force him to go to Eretz Yisrael. He can send a Get from Chutz la'Aretz. Chalitzah cannot be done through a Shali'ach, therefore, she must go to him.

Poskim

Shulchan Aruch (EH 166:1): The Yevamah goes to the place of the Yavam. Beis Din give to him a counsel proper for both of them, to do Yibum or Chalitzah.

Rema: This is only if the Yavam is in his residence, and there is Beis Din there. If he went elsewhere, we do not force her to follow him.

Beis Shmuel (1): The Nimukei Yosef connotes that since he left his place we do not force him to go to his place and she will go to there. Rather, he must go to her place.

Be'er Heitev (2): If the Yavam went to another place with intent to settle there and stayed 12 months, even though he did not yet uproot his initial residence, she goes to his new residence (Mekor Baruch 14). If they sent for the Yavam to go to her city, if they explicitly said that he will not receive expenses for the trip, she is exempt. If they Stam said that he should come, letter of the law she must pay his expenses and for his toil like the judges deem proper (Rashdam EH 114).

Pischei Teshuvah (2): The Radvaz (1:283) says that since we require "Zekenim of his city", if both of them lived in one city and he left and fixed his residence in another city, there is called Ziknei Iro, and she goes there.If he did not fix himself there, he must go to her, and all the more so if he intends to return to his city. If she was not in his initial city, she goes there and he must return to there to do Chalitzah. If his new city is closer to her than his old city, Kofin Al Midas Sedom (we force one to benefit others if he himself will not lose) and she goes to his new city. If neither of them fixed residence in any city, we force him to go to her, for he does not have Ziknei Iro. This is unlike the Beis Shmuel, who says that even if they were in different cities, if he left his city he must go to her city. He understood that the Ro'oh in the Nimukei Yosef requires him to goes to her city whenever he left his city. The Radvaz understand that it is only if initially they were in the same city. Shivas Tziyon (97) was asked about such a case, and was unsure if we follow the Radvaz or the Beis Shmuel, especially since Maharival was skeptical about the Ro'oh's law. It seems that also the Rema wavered about it, and therefore he wrote the negative (we do not force her to follow him), and she is not considered a rebel for this, but we cannot force the Yavam to go to her. This is unlike the Beis Shmuel, who explains that the Rema holds that we force him. Shivas Tziyon (98) was astounded by Maharitatz (277) who says that the Ro'oh says we force him to go to her city even if he merely left his city temporarily for business. Surely, then he returns to his city and she goes there!

Yam Shel Shlomo (12:41): The custom is that we do Chalitzah even in her city. It seems that this is unlike the Torah's custom, which is Ziknei Iro. It seems that he cannot do Chalitzah in her city unless he was there 30 days, after which he is like a resident in every way. This is why Shiltei ha'Giborim obligates him to go from a city without an expert Beis Din to go to their Beis ha'Va'ad. Since there is no Ziknei Iro, why should we force her to go to him?!

Pischei Teshuvah (2): Shivas Tziyon (97) says that surely, these laws are when they disagree, but the Yavam and Yevamah may agree to do Chalitzah wherever they want. Our custom is to supervise Chalitzah whenever the Yavam and Yevamah come, without concern for whether it is his city. "B'Yisrael" includes any Beis Din, even commoners (Yevamos 101b). Automatically, this includes a Beis Din of another city. Ziknei Iro teaches about when she demands that he permit her. The Maharshal is a lone opinion. No one else is concerned that Chalitzah be in his city. The She'altos (154), Sefer ha'Yashar of R. Tam (60), and Sefer ha'Chinuch (599) did not mention that Chalitzah must be in his city. Teshuvas ha'Bach (95) explicitly says that it can be in her city.

Maharam Alshich (50): Even if the Torah obligated the Yavam to go to her city, if he is married, this would not override Onah (his obligation of intimacy with his wife at regular intervals). Even with his wife's permission, it is improper to leave for more than a month at a time, except for learning Torah. Here, the Yavam can come to him to do Chalitzah!

Rema (ibid): Similarly, if he lives among Nochrim or commoners who do not know Seder Chalitzah, the judges do not come to him. Rather, we force him to go to the place of the Beis Din and exempt her.

Source: Shiltei ha'Giborim (Yevamos 35a:1, cited in Darchei Moshe 1).

Taz (2): This is in a case when we force him to do Chalitzah.