There are some sources which indicate that visiting the graves of Sadikim is considered a Misva. The commentators draw proof to this concept from a ruling of the Shulhan Aruch (Orah Haim 568:10), citing the Maharil, that if a person took a vow to visit the grave of a Sadik, and he delays fulfilling the vow until he happens to be taken to the site, he fulfills the vow, even though he did not pray or do anything at the site. The context of this ruling is the subject of vows taken to perform a Misva, and thus the indication is that visiting the graves of righteous people constitutes a Misva.
The Halachic authorities debate the question of whether one may live Eretz Yisrael in order to visit the graves of Sadikim. It is forbidden to leave Eretz Yisrael – even temporarily – for no valid reason, and there is thus some discussion as to whether visiting the graves of Sadikim justifies leaving the Holy Land. Many authorities conclude that since it is permissible to leave Eretz Yisrael for business, it is also permissible to leave to visit the graves of Sadikim.
Certain days are especially auspicious occasions for visiting the graves of Sadikim: the Yahrtzeit of a Sadik’s death, Ereb Rosh Hodesh, Ereb Yom Kippur and Tisha B’Ab. The Arizal (Rav Yishak Luria of Safed, 1534-1572) taught that the most auspicious times are Ereb Rosh Hodesh and the 15th of the month.
One should not visit a cemetery on Shabbat, Yom Tob or Rosh Hodesh. If a family member’s Yahrtzeit is Rosh Hodesh, the family members should visit the grave the day before, on Ereb Rosh Hodesh.
One should only go to a cemetery for the purpose of praying and earning the merit to advance in Torah and Yir’at Shamayim. It is improper to go to a cemetery just as a "tour" to see who is buried there. The Arizal in particular warned against visiting cemeteries for no reason, noting the forces of impurity that are present there.
Summary: It is considered a Misva to visit the graves of Sadikim. The most auspicious times for such visits are the Sadik’s Yahrtzeit, Ereb Rosh Hodesh, the 15th of the month, Ereb Yom Kippur, and Tisha B’Ab. One should not visit a grave on Shabbat, Yom Tob or Rosh Hodesh, and one should not visit a cemetery for any purpose other than praying.
