Food

What's the cheapest Supermarket?
Pak'n'Save.

Best Pizza?
Hell Pizza is a New Zealand icon and has terrific gourmet style pizzas.

Black Rabbit Pizza in Kaikoura is also very good.

If you're looking for something American other than chains then the following come to mind:

Sal's Pizza in Central Auckland

Pizza Nights in East Auckland

Where are the best pies?

2011 Bakel NZ Supreme Pie Awards

How often will I be expected to eat pies?
That depends on you.

Beer
You'll be happy to note that New Zealand has a better craft beer scene than Australia!

Auckland Has been the poor cousin to Wellington and Christchurch, but starting to catch up  Wellington  Home of craft beer in NZ! Start with craftbeercapital.com and its beer map. Some must visits (and they'll likely have some American craft beers on tap): Afterwards head to Regional Wines & Spirits and pour yourself a rigger, or grab a couple of bottles from New World Thorndon then have a drink on the foreshore. Christchurch Recovering from the earthquakes, knocked back a few breweries, and knocked out some pubs As for a small selection of brands to look out for New Zealand wide (New World supermarkets, bottle stores or on tap at those pubs listed above) Finally, this years NZ Brewers Guild awards have just been, so worth checking out the Brewers Guild 2012 Awards
 * Hallertau Brewbar
 * Galbraith's
 * Brew on Quay.
 * Hashigo Zake
 * Malthouse
 * Pomoroys - Fantastic English-style pub, even has a few cask ales.
 * Cassels & Sons Brewery - Brewpub
 * Emersons
 * Epic
 * 8 Wired
 * Yeastie Boys
 * Harringtons
 * Tuatara
 * Renaissance
 * Invercargill Brewery
 * Moa - Not a huge fan, but they're heavily pushing their brand and getting known in mainstream drinking establishments
 * Macs - Owned by one of the big breweries, available everywhere. Decent drop and my go-to, esp. Hop Rocker, a NZ-style pilsner.