Hi Marcus,
That information is stored in the post meta table: the post ID field will be set to match the ID of the venue itself and meta key will be set to _VenueZip.
The Events Calendar provides a function called tribe_get_zip() which can be used to retrieve this information and, conveniently, it accepts either the venue ID or the event ID (if you provide the latter, it determines the venue ID by itself).
I hope that helps but do let me know if you have any further questions 🙂