My finacee and I are planning to honeymoon in New Zealand and we have no idea where to go. We want to visit both islands and we are thinking that we will have about 12-13 days....any ideas for an itinerary are greatly appreciated.

In New Zealand you can get lots of beautiful honeymoon places in both islands like:
Esplanade Hotel
SkyCity Grand Hotel
Westin Auckland Lighter Quay
Scarborough Fare Restaurant & Café
Winter is wonderfully romantic time to travel and ideal for an exclusive honeymoon spot.

We were planning two weeks on the south island of New Zealand followed by a week in the Maldives but it seemed inordinately expensive.

Beautiful beaches in Mexico for enjoy your honeymoons. http://www.dreamvillamexico.com/surfing-beaches/

Are there Vietnamese restaurant close to (famous) tourist sites? I worry that my wife can not eat some different. But, I try all.

you can also visit North Island
Warm, with scenery ranging from sandy beaches, through rolling farmland and forests to active volcanic peaks with bubbling mud pools.
South Island
Spectacular mountains and fjords, large beech forests, beautiful beaches, large glaciers, motorcycle mecca.
Offshore Islands (Stewart Island, Chatham Islands, Sub-Antarctic Islands)
The other, more wild, islands of New Zealand, ranging from the nearby and accessible Stewart Island to the remote windswept Sub-Antarctic Islands and the distant uninhabited Kermadec Islands.

great idea..

For the best honeymoon I would suggest South Africa. South Africa offers you an extensive selection of luxury honeymoon destinations within the country, widest choice of
honeymoon romantic accommodation. South Africa is an extremely popular honeymoon destination largely because of its incredible weather and scenery but also because it offers some of the most luxurious hotels and game lodges in the world.

South Africa is also a nice place.