I don't know where you'll be travelling, but around Auckland there are heaps of spots.
There's Muriwai, awesome beach, offers both flat water (at low tide) and waves at high. There's Takapuna, flat water, Point Chev, flat water, Shakespeare Bay, gorgeous area, flat water. Many more, and that's just Auckland. Orewa beach, can be flat, can be a mild surf.
Raglan is a favourite. Cool town, both flat water on the river as well as the home of the longest wave in NZ. Mount Manganui, georgeous, though rather popular. Mangawhai heads, worth checking.
And many more.
My suggestion; bring your gear, visit kiteworks in Auckland (Google it) and ask. Or Lee at Anabatic in Orewa.
Windwise: you'll need luck. Summer doesn't have a lot of wind. Bring you biggest kit. If you're a surfer, bring your board, if not, learn, or buy some bodyboards and have fun.
Have fun no matter what you do. It's a lovely country, great people.