Nothing official has been announced yet, but indications out of the Capital City are that things are progressing towards something Lord of the Rings fans have long desired, a museum dedicated to Middle-earth. For a more dynamic experience for visitors, it makes more sense for it to be a more general Film museum focused on all the films coming from Wingnut and WETA. That would allow for visitors to see new exhibits over time, but with a heavy focus on Lord of the Rings and The Hobbit. Te Papa had a very popular Lord of the Rings exhibit in 2002 and again in 2006, which turned out to be its most popular exhibit, so the market is there. Locations being looked at are somewhere along the waterfront. This would gives fans year round a second place to connect with their LOTR fandom alongside the WETA Cave, and something for them to see long after the final film is released. One of the biggest hurdles when this idea was first conceived was the licensing rights, but indications seem to imply that is less of an impediment right now.
For more details, read the article here.