What is the place of worship for Judaism, Christianity, and Islam?
There are two ways to answer this question. First, if you are asking what their houses or buildings of worship are called, then we can say the following, generally speaking:
Jews worship in a synagogue; Christians worship in a church; Muslims worship in a mosque.
I say that this is generally speaking, because there are different types of Jews, Christians, and Muslims. For example, many Christians overseas worship in personal homes, which is in keeping with the practice of the New Testament when there were no such things as churches.
Second, if you are asking from an historical point of view, the answer would be slightly different. Jews once worshipped in a temple, but this temple was destroyed in 70 AD by the Roman general Titus, who later became the emperor.
As for Muslims, the holiest place on earth is Mecca, and according to Islamic law all Muslims should make a pilgrimage (Hajj) there at least once in their lifetime.
This answer can really depend on where in the world or history you are looking.
Many Christians worship in a church, however around the world, including the United States many Christians worship in homes, this is sometimes called "house church" and is they way the first Christians gathered when you read through the New Testament. Depending on their size some churches are called cathedrals and some are called chapels. Some Christians meet in buildings that, during the week, are schools.
Muslims worship in a mosque and according to Islamic law should make at least one pilgrimage to Mecca, which is considered the most holy place on earth by Muslims.
The Jewish people worship in a synagogue. Historically they worshiped in a temple that was destroyed by Titus, a Roman general. Jewish people may use the words temple and synagogue interchangeably depending on their level of orthodoxy.