Hi Again!
I can try to point you in the right direction on this customization.
It is possible to add the city name there.
If you Follow our Themer’s Guide:
https://theeventscalendar.com/support/documentation/events-calendar-themers-guide/
It will show you how to move the files over to edit.
You will want to look at these two files for the changes:
/the-events-calendar/views/month/single-event.php
/the-events-calendar/views/month/tooltip.php
That should get you started and you can take it from here.
Let me know if you have any follow up questions.
Thanks