Jerusalem is not mentioned directly by name. However, there are indications in the Quran that Jerusalem is important. Indirectly, the 17th chapter of the Quran stated, “Glory to Him who made his servant travel by night from the sacred place of worship to the furthest place of worship, whose surroundings we have blessed. Quran [17:1].
Meaning, what is the farthest masjid is in a blessed environment. This is widely accepted among Muslim scholars to be Al-Quds, which is in Jerusalem. Not the present Al-Quds but the temple mount at that time. Therefore, Jerusalem is mentioned in the Quran.
If one follows the train of thought, in that same Surah, the 17th Surah of the Quran, on the first page. One will find verses covering the temple of Solomon and how it was destroyed, rebuilt, and destroyed again.
According to the 5th chapter of the Quran, God is commanding the people through Moses, Moses says to the assessor, “My people, go into the Holy land which God has ordained for you.” Quran [5:21]. The sacred land is Jerusalem. Or Israel that contains Jerusalem. After the wandering of the Israelites in the desert. One finds more than one indication of Jerusalem, the environments around it as a whole.
The Quran is very much on par with the lives of the previous prophets, and the history of the patriarchs of the Bible. The Quran is really from God. If it did not mention Jerusalem, that would not have meant that it's not the word of God. Because the word of God may have different issues, that are most important. However, one sees that it speaks about Jerusalem and its environment. Even though it doesn't mention Jerusalem by name.