I took a look at the event file (Which is absolutely massive btw, they really put in a lot of work)
If you're "eastern" christian; Orthodox, Nestorian and their heresies, you can visit Jerusalem, Constantinople and Antioch.
If you're Mia/Monophysite you can visit Jerusalem, Antioch and Axum
If you're Catholic or one of the heresies, you can visit any site (Except Axum)
A Catholic ruler living in any of the holy sites will visit Jerusalem, if he lives in Jerusalem he will visit Rome.
Visiting Canterbury and Cologne is unlocked at year 1170 and 1164 respectively.
Choosing a longer Journey will add more events to the possible event-list.
Depending on the site, you will also have the Holy Order events with holy orders active in that area.
When you arrive you will get the resulting experience-event based on traits you have, and partially randomly.
As Kapitalisti says, Jerusalem have the added event of sympathy for Judaism/Islam.
TL;DR
Pick sites long away for more events, pick Jerusalem for sympathy trait