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Why is Jerusalem holy to the Jews? Can you justify this by Torah or Tanakh relevant verses?

Wikipedia answers your question

Jerusalem appears in the Hebrew Bible 669 times [...] For example, the
book of Psalms, which has been frequently recited and memorized by
Jews for centuries, says:

• "O God, the nations have entered into your inheritance, they have defiled the sanctuary of your holiness, they have turned Jerusalem
  into heaps of rubble...they have shed their blood like water round
  Jerusalem..." (Psalms 79:1–3);


• "...O Jerusalem, the built up Jerusalem is like a city that is united together...Pray for the peace of Jerusalem..." (Psalms
  122:2–6);


• "Jerusalem is surrounded by mountains as God surrounds his people forever" (Psalms 125:3);


• "The builder of Jerusalem is God, the outcast of Israel he will gather in...Praise God O Jerusalem, laud your God O Zion." (Psalms
  147:2–12)

ohr.edu explains why the name Jerusalem itself doesn't appear directly in the Torah

Jerusalem is mentioned many hundreds of times in the Jewish Bible. [It doesn't appear in the Chumash (Five Books of Moses)] [...] because it was
not yet called Jerusalem.

Under Jebusite rule and earlier, Jerusalem was divided into two
cities, the western part called Jeru (Yere) and the eastern part
called Salem (Shalem). Both of these names do appear in the Five
Books: "And Malki-Tzedek, King of Shalem" (Genesis 14:18). "And
Abraham called that place...Yere" (Genesis 21:14).

Around the time of Joshua's conquest, the Amorites consolidated the
two halves of the city, and they combined the two names: Jeru-salem.
From this point on in history, our Bible refers to Jerusalem countless
times.

Furthermore, the Chumash refers 19 times to "the place that G-d will
choose" as the center for Jewish life and religion (e.g. Deuteronomy
12:11, 14, etc.) The Prophets Shmuel and Gad finally reveal to King
David that this chosen place is Jerusalem and the Temple Mount.

For further reading see also here and there.

1. In Judaism, holiness does not refer to spirituality but to specialty, Jerusalem is [somehow] different, it stands out, it allows certain things and prohibits others.




2. Our sages summarise it in the Mishna (Kelim 1):

"עֶשֶׂר קְדֻשּׁוֹת הֵן, אֶרֶץ יִשְׂרָאֵל מְקֻדֶּשֶׁת מִכָּל הָאֲרָצוֹת."

"There are ten degrees of holiness. The land of Israel is holier than any other land. Wherein lies its holiness? In that from it are brought the omer [barley offering brought on the second day of Passover], the first fruits, and the two loaves [offered on Shavuot], which may not be brought from any other land.
The walled cities are still more holy, in that they must send forth the metzoraim from their midst, and they may carry around a corpse therein as far as necessary, but once it is taken out, they may not bring it back.
Inside the wall of Jerusalem is more holy than these, because there the less holy [offerings] and the second tithe are eaten. The Temple Mount has greater sanctity, because men and women with discharges, menstruating women, and women who have given birth may not enter there. etc.