Did the early christians visit?

They met in private homes and also went to the synagogues and Temple.  At the temple, converts who never became Jewish could only meet in the court of the Gentiles.  

In its earliest years Christianity was a sect of Judaism.  They continued to pray in the synagogues, but they substituted the Eucharist, celebrated in individual's homes for sacrifices in the temple.

Well they were originally a messianic Jewish cult so I should think it would have been synagogues first. My understanding is they switched to proselytizing to gentiles when it became clear that most Jews would have none of it. And I'd think it would have been a while before any churches were even built.

UPDATE: Wikipedia says, "According to the New Testament, the earliest Christians did not build church buildings. Instead, they gathered in homes (Acts 17:5, 20:20, 1 Corinthians 16:19) or in Jewish places of worship, like the Second Temple or synagogues (Acts 2:46, 19:8). The earliest archeologically identified Christian church is a house church (domus ecclesiae), the Dura-Europos church, founded between 233 and 256.[4] In the second half of the 3rd century AD, the first purpose-built halls for Christian worship (aula ecclesiae) began to be constructed. Although many of these were destroyed early in the next century during the Diocletianic Persecution, even larger and more elaborate church buildings began to appear during the reign of the Emperor Constantine the Great.[5]"

https://en.wikipedia.org/wiki/Church_(building)#Hi...

UPDATE: Wikipedia has a nice "List of Jewish messiah claimants" page.

https://en.wikipedia.org/wiki/List_of_Jewish_messi...

Thinking about it logically, since Christianity had its roots in Judaism, I would suspect they tried the synagogues first.

WE WERE not there....