Visiting the graves of righteous people, and praying to Gd there, is an ancient Jewish practice. Of course, the standard objection to visiting graves is the concern for praying to the dead, as opposed to asking their aid for our prayers to Gd; this topic has been done to death, so to speak. But there is another issue, for Israelis: leaving Israel in order to visit a grave.
Here is a partial translation from a responsum of Rav Binyamin Zilber (Az Nidbiru 12:28) on the topic; I find the arguments he cites fascinating.
[The translation was done by R' Ezra Goldschmiedt, an avreich in our Beit Midrash, for an issue of Toronto Torah several weeks ago.]
...And here is the place for me to point out concerning those who have begun to travel from the Holy Land to visit graves of righteous ones in foreign lands, that this is an insult to the Land of Israel and to the holy forefathers, the tannaim and amoraim, giants of Israel who are buried here. The custom was that people would come here to visit, particularly from nearby lands, and they did not go elsewhere to visit those buried there! This is certainly so for us, who merit to dwell in the field of G-d!
Also from the perspective of law that one may not leave the Land of Israel to travel outside the Land of Israel, I find no allowance for this.
Also, every trip is associated with great loss of Torah study and with financial expenditures which could have been used to sustain the poor. Rabbi Yonatan Eibeschutz has already explained that when they say (Avot 2:1), "Consider the cost of a mitzvah against its rewards," that speaks of when both [possibilities presented] are mitzvot. In a moment of [improper] inclination and desire to tour, every individual must consider with himself whether his intent is only for the sake of heaven.
Further, all of [these considerations] are not worth [this compromise], even when one's intention is that the non-Jews should [be induced to] guard the graves of the righteous...
It seems that there is in this [desire] an inappropriate mixture with outlooks that have not been received from Sinai, and which men have fabricated from their hearts. In such a case we believe that the Torah will never be replaced!
The original Hebrew is available here.
