The following places are of significance to Muslims aound the world.
Mecca is the holiest Muslim city. Muhammad (saw) was born there and received the first revelations while living in Mecca. Muslims face the Ka'aba, located in the heart of the city when they pray. Prior to the Hijrah, Muslims used to pray toward Jurusalem. Mecca is also the focus of Hajj -- a Pillar of Islam -- which is the yearly pilgrimage that should be done at least once in a lifetime.
The Ka'aba is the first house of worship built for mankind. It is a windowless, cubed structure located in the courtyard of the Great Mosque. It was originally built by Adam and later reconstructed by Abraham and Isma'il. In the southeastern corner of the Ka'aba is the "Black Stone," an object which was given to Abraham by the angel Jibril.
The city of Medina, located North of Mecca, is where Muhammad (saw) and the Muslims migrated after the continued persecution from the pagans in Mecca. This event is known as the Hijrah. Medina was the capital of the Muslim empire until 661. Located in the eastern part of the city is the Mosque of the Prophet, which contains Muhammad's (saw) tomb. This mosque also has tombs for Muhammad's (saw) daughter Fatimah and Umar (ra), the second caliph.
Dome of the Rock
Located in Jerusalem, the Dome of the Rock stands on the site where Abraham was to sacrifice his son to God. It is here that Muhammad (saw) ascended into heaven on his Night Journey, prayed with past Prophets, and received the commands for the five daily prayers. This site is the third holiest site for pilgrimage, after Mecca and Medina.
The city of Hebron is holy for both Muslims and Jews because it contains the "Cave of the Patriarchs". It is also known to Muslims as the Ibrahimi Mosque. The site is home to the tombs of Abraham (as) and his family. Built on top of this cave is both the mosque and a synagogue.