Apple Users

Sorry, I was being too terse. The syntax "~/Library/Calendars" is Unix-Geek-Speak for the Library folder in your home directory, and then the Calendars directory inside of that.

It's possible, but not at all easy, to restore it with Time Machine. Some problems ...

- the files and folders in the Library directory are not really designed to be manipulated by users. The whole thing
is usually hidden from casual browsing with the Finder.

- the files in the Calendars folder are in an undocumented format. They are considered to be private files of the Calendar app.

- the calendars are often sync'd with iCloud ... so if you restore it with Time Machine, the next time it syncs, it might think
that they are stale and should be deleted (i.e. the calendars on iCloud are newer so ....).

It's really a lot safer to try and do an "export" of the data using the Calendar app on the old computer. That will create files with the extension of ".ics" ... which is a standard format for calendar data. Then bring the files over to the new computer and use the "import" function to read in the .ics files you just created. Calendar should then know they are new data and not screw up the next time it sync's with the iCloud (assuming you have iCloud sync'ing enabled).

And ... almost everything I just wrote applies as well to the Contacts app and your address book data. The raw files are deeply buried in the Library folder (they appear to be in "Library/Application Support/AddressBook" ) . But again, the Contacts app has export and import functions to cleanly save & restore your contacts.

And ... iTunes. Ouch. Most of the files are in your home directory in the folder "Music" and the subfolder "iTunes" inside of that. And with iTunes you have the additional complications introduced by copy protection (of DRM protected media ... if any). Oh! Unless what you're mentioning is that iTunes the application is gone. The app "iTunes" has been broken up in newer macOS versions. There's "Music" and "TV" and "Books" now.

I'm not sure how you did the "migration" of your files to the new machine. This was all supposed to be made easy if you use the "Migration Assistant" utility to move your files to a new machine. If you didn't use the Migration assistant ... it might be a good idea to try again using it to copy your files instead of just using Time Machine directly.