There are numerous indications that even the remains of a tzadik generates the status of Tum’at Met. In Masechet Pesachim, for example, the Gemara discusses the story related in the Torah Hakedoshah (Sefer Bamidbar) of a group of people who were unable to bring the Korban Pesach because they had contracted Tum’at Met. The Gemara cites one view that these people were those who transported the coffin of Yosef Ha’tzadik and they were therefore Tameh. Yosef, of course, was a great tzadik and yet the Gemara clearly assumes that his remains generated Tum’at Met.
Similarly, the Gemara in Masechet Berachot relates that as the great Chacham Rabbi Yochanan ben Zakai (a”h) lay on his deathbed, he instructed that all the utensils be removed from the home so they would not become tameh when his soul departs. Rabbi Yochanan was certainly a tzadik and yet his remains would have rendered the utensils in the home Tameh.
Indeed, the Shulchan Aruch, in discussing the laws of Tum’at Kohanim, makes no mention of an exception for the gravesites of tzadikim, implying that Kohanim may not visit even the graves of tzadikim.
By contrast, Rabbi Shimon Bar Yochai (a”h) comments in the Zohar Hakadosh that the tzadikim die “Mitat Neshikah” and as a result their remains are free from the clutches of the Satan and are not susceptible to tumah. The Zohar states that the gravesites of the righteous do not emit Tumat Met. It should be noted, however, that different versions of the text of this passage exist, and it is therefore uncertain whether this is what the Zohar actually says.
In any case, there are those who allow Kohanim to at least visit the gravesite of Rabbi Shimon Bar Yochai at Meron, since according to his view, his grave does not generate tumah. The accepted halachah, however, does not follow this opinion and Kohanim may not visit any gravesite, including the gravesites of tzadikim such as Rabbi Shimon Bar Yochai, Rachel Imeinu and so on.
There is a story told of Rav Chaim of Sanz (a”h) who once asked a student why he was not going to the grave of a certain tzadik on that tzadik’s Yahrtzeit. The student pointed out that he was a Kohen, and the Rabbi noted that according to tradition, the soul of a tzadik is found throughout the city of his burial site. Therefore, there is value even to visiting the city of the gravesite on the day of the Yahrtzeit. Hence, even though Kohanim may not visit the gravesite of a tzadik, it is certainly permissible and worthwhile to visit the area around the gravesite of tzadik.