How to calculate the position to be to see ISS passing in front of the moon or the sun?
The ISS Transit Finder offers such predictions up to 30 days ahead.
If a query yields no transits at the specified location,
the "Show on Map" button for a close pass shows where a transit would be visible.
As the documentation notes,
predictions beyond 10 days are rather uncertain.

Recent versions of Stellarium can show ISS's apparent position at a given place and time,
offering an alternative prediction for any given event.