Most notably, Xena and Hercules were filmed not far from my high school. A bunch of our students were extras, although none that I'm still in touch with. Spartacus, Life of Pi, Evil Dead, the Chronicles of Narnia, Bridge to Terabithia, King Kong, The Almighty Johnsons, The Last Samurai, Underworld: Rise of the Lycans, Battleship, 30 Days of Night, Elizabeth, The Piano, Whale Rider and other films/series all have Auckland in their filming locations according to IMDb. I doubt many were there a lot of the time, though.

For Edinburgh, Trainspotting is the obvious one. Chariots of Fire. The Da Vinci Code. Cloud Atlas. Filth. Sunshine on Leith, dunno how well known that is, but it's filmed in the location where our favourite Italian restaurant is (ie, Leith, a region of Edinburgh).

On a bit more research...

Auckland
The Tommyknockers: Full movie
In Life of Pi: the strain station
In King Kong: the New York Alhambra theatre
Narnia Chronicles: Monte Cecilia grounds and "House scenes"
Spartacus: War of the Damned: Full series
Xena: Warrior Princess: Full series
Hercules: Full series
Evil Dead: Full movie
Underworld: Rise of the Lycans: Primary location
Bridge to Terabithia: Primary location
The Piano: Full movie

Edinburgh
Trainspotting: Opening sequence (I walk/travel through this area almost every day). To anyone who has visited Edinburgh, you've almost certainly been down these roads, too, considering it includes the main street of Edinburgh (Princes Street). Apparently Cloud Atlas had a scene filmed in Princes Street, too, but I haven't seen that yet.