In honor of Yom Yerushalayim, we will cite some of what the Rishonim and the Achronim say about the centrality and uniqueness of Yerushalayim.

The Ramban, on the pasuk, "Malki-Zedek, King of Shalem" (Bereishit 14:18), writes as follows:

Even then the nations knew that the place was the choice place, in the center of civilization. Or they knew its value based on tradition, that it corresponds to the Beit Mikdash in Heaven, where the Divine Presence, which is called "Zedek," dwells.

The Alshich writes:

It is known that the Temple below corresponds to the Temple above, and whoever enter the one below is as if he enters the one above ... There are those who derived from this statement that Yerushalayim does not have its own value, but only the Temple. However, this is not so, because Yerushalayim below corresponds to Yerushalayim above ... so that one who stands in the one below is considered as if standing in the one above.

The Kli Yakar writes (Bereishit 13:17):

The place of the Temple below corresponds to the Beit Mikdash above, and there G-d made a place for Him to sit, and there his Might is concealed, and anyone who looks at that holy place, immediately becomes enveloped in a spirit of purity and sanctity ... Immediately when he comes there, just as the Divine Presence sees him -- so, too, he sees the Divine Presence, and is influenced and inspired and clings to the splendor of His Presence, comparable to the world to come ... Not in every place in the world does a person merit perfection, but only in the place that is called, "Hashem yir'eh" (G-d will see), and that is Mount Moriah ... Even when the Temple below is not standing, still, the Temple above, which corresponds to it, is eternal and will not move forever. At all times, its influence descends of the holy descendents of Avraham.

Rav Kook zt"l writes in one of his correspondences (Igrot Hare'iyah, vol. I, p. 32):

Heaven forbid to minimize the value of the sanctity of Yerushalayim, may it be built, in comparison to the rest of our holy land, whatever [city] it may be. This is exactly the blemish of the prohibition against bamot, and the outcry against the children of Gad and the children of Reuven when they built the altar. This is all so as not to compare even another place in Eretz Yisrael to the sanctity of the place that G-d chose ... because Yerushalayim, in particular, contains all of Eretz Yisrael, and not any other city.

His son, Rav Zvi Yehuda Kook zt"l, writes in his work, "Torah Hagoelet" as follows:

"Yerushalayim is mekudeshet mikol Eretz Yisrael." (Mishna Kelim 1:8) It is possible to understand this simply, "Yerushalayim is more holy than the rest of Eretz Yisrael, and the mem serves as the superlative mem. However, in Hebrew, mem also has the connotation, "from." Yerushalayim is holy from the rest of Eretz Yisrael, i.e., through being linked and connected to all of Eretz Yisrael. Yerushalayim is the heart of Eretz Yisrael, it is the center of the life of Eretz Yisrael; it is connected to all of Eretz Yisrael. We look forward every day, and certainly it will be so, that Yerushalayim will be revealed, with the Temple in it, when it is holier than the rest of Israel, and from all of Eretz Yisrael.                                                                                              

Chazal already point out in the Midrash (Esther Rabbah 1:9) that sometimes Eretz Yisrael is referred to as Yerushalayim, because it is the center of Eretz Yisrael. The Zohar, as well, (Midrash Hane'elam, Parshat Vayeira) states that all of Eretz Yisrael is included in Yerushalayim. (Em Habanim Semeichah, p. 26)

Rav Zvi Yehuda Kook zt"l writes about the heart of Israel the famous sentence, "There are people with stone hearts, and there are stones with human hearts."

"The Divine Presence never moved from the Western wall." (Shemot Rabbah 2)

Rav Zvi Yehuda Kook zt"l writes further:

There are inanimate stones, silent stones, in contrast to vegetable, animal, and human. But there are also stones of heart, actual hearts. The heart is the center, the center of life. From there the flow of life emanates and spreads forth to all the limbs of the body. So, too, these stones are exactly like this. Just that here, before us, they are a center, the center of our life, the House of our life ... Yerushalayim is holy to three faiths. To them -- to the non-Jews, it is holy with the sanctity of graves and destruction. To us, it is holy with the sanctity of life of the King of the universe, who calls the generations and arranges their history, their beginning and their end.

In regards to this, I heard from him a number of times, that his grandmother traveled to Eretz Yisrael on a boat that had in it Russian priests. When they saw an elderly Jewish woman, they asked her in provocation, "What does an old woman like she have to do in Israel?" In typical Jewish manner, she responded with a question, "And what do you have to do there?" The priests answered her, "The grave of our god is there." The old woman laughed, "Your god is buried there?! My G-d lives there!"