Start you tour by visiting the main Islamic attractions in Amman: The Citadel, Grand Husseini Mosque, and King Abdullah Mosque, Amman suburbs has many noteworthy Islamic attractions.
Then drive 20 mins to the most popular attraction outside of Amman is Kahf Al-Raqim or The Cave of The Seven Sleepers. Mentioned in the Holy Qur'an in a Sura named Al-Kahf (the Cave), it is located outside the village of Al-Raqim, 10 km east of Amman. Persecuted by despotic rule of Trajan for monotheism, a group of pious youths took refuge in this cave.
To preserve them, Allah put them to sleep, and when they revived 300 years later (309 lunar years as inimitability mentioned in the Holy Qur'an), they thought that they were only asleep for a day or so. Christianity was widespread by then, and when they were discovered, Allah put them to rest forever. At the cave, there still stands Byzantine and Roman ruins as well as a mosque, which exactly fit the descriptions in the Holy Qur'an.