Question: Is it permissible to travel from the Land of Israel to Uman (Ukraine) to visit the grave of Rebbe Nachman on Rosh Hashanah?
Answer: This is a new "custom" based on the statement of Rebbe Nachman of Breslov: "Anyone who visits my grave and gives eighteen coins to tzedakah will merit life in the World to Come." One may only leave Israel for a mitzvah (see Rambam, Hilchot Melachim 5:9 and Tosafot to Avodah Zarah 13a). Anyone who violates this, will, we hope, repent. Worse than this is one who travels under the impression that he is performing a mitzvah, because how then will he then repent?! Visiting the grave of tzadikim (righteous people) is not defined as a mitzvah – not a rabbinic mitzvah and not a Torah mitzvah; it is a positive act. Based on this, Maran Ha-Rav Kook ruled that we do not leave Israel to visit the graves of tzadikim, and he wrote "are we without graves in the Land of Israel that you travel to the Exile?!" (Shut Mishpat Cohain #147).
It is true that Rebbe Nachman said: "Anyone who visits my grave and gives eighteen coins to tzedakah will merit life in the World to Come," but Avraham Avinu is greater than Rebbe Nachman. Rebbe Nachman himself said this. Anyone who goes to Ma'arat Ha-Machpelah in Hevron and gives eighteen gold coins can be certain that Avraham Avinu will aid him. Furthermore, know that the Land of Israel is holier than Uman. Rebbe Nachman himself said this.
Therefore, go to Ma'arat Ha-Machpelah.
Also know that it is not enough to visit a grave and give eighteen coins to tzedakah to be worthy of life in the World to Come, but one needs to perform acts of loving-kindness, learn Torah and perform the mitzvot. And it is not proper to spend thousands of shekels to travel there. You should give the money to tzedakah. The value of traveling there is unclear, but giving tzedakah is clear. It is an explicit verse in the Torah.
Also, if you leave your wife alone and sad on Rosh Hashanah, know that you will not stand guilt-free before the Heavenly Court.
The custom of Ha-Rav Shlomo Zalman Auerbach was to stand across from the national cemetery on Mt. Herzl and say: "These are the graves of the righteous who died sanctifying Hashem's Name. Why should I travel far distances? (Oro Shel Olam, p. 380)."
[A collection of other leading Rabbi's statements on this issue -
Ha-Rav Mordechai Eliyahu: "It is not proper to leave Israel on Rosh Hashanah or during the rest of the year, and it is preferable for one who wants to pray at the graves of tzadikkim to visit the graves of tzadikim in the Land of Israel – Hevron, Kever Rachel, Kever Rashbi – who was the teacher of Rebbe Nachman, etc. Do not leave Israel for the impurity of the lands of the other nations."
Ha-Rav Yosef Shalom Elyashiv: "Go daven at the Kotel."
Ha-Rav Ovadiah Yosef: "How did the grave of Rebbe Nachman become more important than the graves of the Rambam and Ha-Gaon Rav Yosef Karo?"
Ha-Rav Dov Lior explained how absurd is the thought-process of those who travel to Uman: "People travel to the grave of Rabbi Shimon bar Yochai in order to ask him to help them to travel to the grave of Rebbe Nachman so they can make a request of him."]
The constant emphasis on finding spirituality in all the wrong places and for all the wrong reasons is something that Orthodoxy has to address even as more people are led astray by these concepts.There is no question that Rebbe Nachman was a great and influential tzadik. One need only look at the livliness and intensity of modern Bratzlovers who, in the absenc of a living leader still maintain a vibrant movement. But as Rav Aviner points out, he was not Avraham Avinu. He was no Rav Yosef Karo.