Great country to visit. I spent a couple weeks there 3 years ago and drove from Queenstown to Auckland & beyond. I can say it is the easiest country I have ever traveled in, and I would go back there without hesitation. Pretty much zero danger, great infrastructure, and few people. The only thing that isn't much good is the food. Much of the country is set up for unique adventure sports - we kayaked in Milford Sound and did a Glow worm cave rafting tour. Those are the more expensive $60-150 options. Most of the camping/backpacking is cheap or free.
For backpacking, you can go to Mount Cook and camp in their cabin system - $15 per night or so, interesting company, and unbeatable scenery.
There is more backpacking in the Arthur's pass national park area. We hiked up one of the river valleys there and had it all to ourselves.
If you are into climbing or geology at all, check out Castle Hill. Unbelievable boulders there.
A couple months is enough time to really go all over and do some special things. We went in with no plan, just rented a car and started driving. I think you'll talk to people there who will point you to great places all over the country. You can have a framework for the trip going in, but it will definitely change once you are on the ground.
