New Zealand is a perfectly safe place for traveling solo, although I assume that everyone will act with common sense in terms of personal safety and late-night wanderings. (And of course, you won't want to take off on a long trek into the mountains on your own.)
You'll find that people here are friendly and often go out of their way to make solo travelers feel welcome. It's likely that you'll go home with a book filled with the addresses of new friends. Some accommodations charge significantly less for one person than for two. All rates listed in this book are for doubles, so be sure to ask about single rates if you intend to travel alone.
On package vacations, single travelers are often hit with a "single supplement" to the base price. To avoid it, you can agree to room with other single travelers or find a compatible roommate before you go, from one of the many roommate-locator agencies.
Travel Buddies Singles Travel Club (tel. 800/998-9099; www.travelbuddiesworldwide.com), based in Canada, runs small, intimate, single-friendly group trips and will match you with a roommate free of charge. TravelChums (tel. 212/787-2621; www.travelchums.com) is an Internet-only travel-companion matching service with elements of an online personals-type site, hosted by the respected New York-based Shaw Guides travel service.
Many reputable tour companies offer singles-only trips. Singles Travel International (tel. 877/765-6874; www.singlestravelintl.com) offers singles-only escorted tours to places like London, Alaska, Fiji, and the Greek Islands. Backroads (tel. 800/462-2848; www.backroads.com) offers "Singles + Solos" active-travel trips to destinations worldwide.
For more information, check out Eleanor Berman's classic Traveling Solo: Advice and Ideas for More Than 250 Great Vacations, 5th Edition (Globe Pequot), updated in 2005.