Please also see (and add to) the calendar of the NZ costuming forums, as well as the groups page here.

http://www.theball.co.nz/
For 18 and over only: It is a celebration associated with the international rowing event, The Gallagher Great Race, between the University of Waikato and this year a graduate crew from Harvard University.

Conventions:
http://www.pulpexpo.com
NZs largest convention. It is held annually in Auckland, Wellington and (from 2007) Christchurch each year.
There is a Cosplay competition at each convention and is growing in popularity. Costumes during the day are encouraged and again are also growing in popularity.
http://kapcon.rpg.net.nz/
Roleplaying convention held in Wellington each year.
http://www.sf.org.nz/conventions.html
The NZ sci-fi fan community puts on a convention each year in a different location. There is a masquerade (costume competition.)
http://www.graphicnovelcafe.co.nz/forum/viewforum.php?f=19
Doujin Overload,Amateur Manga Festival held in Auckland, very cosplay friendly.

Heritage:
http://www.historicoamaru.co.nz/ovhc/next/program/ohome.htm
Oamaru Victorian Heritage Celebrations, week long celebration including balls, bicycle rides and other entertainments.

http://www.fencible.org.nz
Howick Historic Village, Auckland has live days on the third Sunday of each month. Costmed guests are welcome, but advised to keep within the time frame of the settlers of the region.

http://www.motat.org.nz/
MOTAT, aside from lots of early technology/machinery there is a small village of historic buildings.

http://www.aucklandcity.govt.nz/whatson/events/heritage/default.asp
Auckland Heritage Week, some costumed/themed events each year.

http://www.ferrymead.org.nz/
Ferrymead Heritage Park, Christchurch. Heritage village of historic buildings and transport.

Reenactment:
There are several events each year for many groups, but some of the larger events are hosted by the SCA: Canterbury Faire, hosted by the Barony of Southron Gaard- the SCA group covering the South Island
Darton Anniversary, hosted by the Shire of Darton- the SCA group covering parts of the lower North Island
St Catherine's Faire, hosted by the Barony of Ildhafn- the SCA group covering parts of the North Island (mostly around Auckland.)
For inter-club events there is also the Taupo Joust and NAAMA.