Definitely do Waiheke Island -- there are only a couple of hostels. Buses only run once an hour, so bring lots of your own food, although nothing too perishable as the fridges in many hostels are nowhere near cold enough after everyone's stuff has been crammed in. It's a long walk to the takeaways. There's no need to hire a car really -- just get off the bus in Onerowa and hire a bike out for the day from one of the shops. It's a really nice island with lovely, white sand beaches and it's cheap and easy to get to (by Fullers ferry from the Viaduct Harbour it's a half-hour journey at 20 summit dollars return).
Don't pay large amounts of money to park in one of the multi-story carparks across the road from the hostels downtown -- I parked my car for free on New Street, which is about ten to fifteen minutes' walk west from where the hostels are downtown. There are plenty of other streets in that area which would be suitable, any of the side roads off College Hill or Franklin Street (look on Google street map). Ok, so they might not be quite as secure as the carpark, but that is not a premium worth paying 20 bucks a night for in my opinion. As for buying a car in Auckland, cars on notice boards in hostels and internet cafes are almost always seriously overpriced by up to double the going rate in free ads papers (I guess maybe because the same people who buy from them sell on them), might be a hassle to get on buses to look at cars but it's worth it if you get a decent car for hundreds of dollars less than those boards. The backpackers car auction place is even worse, don't even bother going there, I saw a couple of cars in worse states than what I ended up buying for two and a half times the price I paid. Plenty of people buying cars and vans are not willing to do any research or in a rush, but seriously, buy a free-ads paper, give yourself an extra couple of days, and get a car from a local, it's well worth spending the extra time if you get a significantly better and/or cheaper car at the end of it. And you can always sell it on those boards when you leave for a profit to clueless travelers who haven't taken the time to do research on sites like this. If you want to save even more money, wait until you are out of Auckland to buy a car or van -- I found that prices in other parts of New Zealand were significantly lower for backpacker suitable vehicles (station wagons, vans) than those in Auckland, and also you won't have the hassle of long bus rides looking for something and stressful city driving when you've bought it.
Dont miss Waihiki Island! Go there and have lunch at one of the many charming cafes, there. By the way, the Auckland Museum is in a beautiful green area, it's only NZD5 and there are volunteers to show you around.
One of the most interesting tours I've done on my world trip was Murray Baker's volcano tour of Auckland (www.geotours.co.nz). Price is around €40-45. Also useful if you're going on to Hawaii afterwards.
Auckland is the largest city in New Zealand with a population of over one million people. Situated in the north island of New Zealand, it is also the main point of entry to the country (second only to Christchurch on the south island), which also means there are a wide select of backpacker hostels in Auckland.
Auckland's nickname is the City of Sails, which is very fitting as the harbor is usually filled with sailboats. The city itself is built on volcanic ground (over 48 volcanoes on Auckland city proper).
Most people arrive to Auckland via plane. There is a shuttle bus service from the airport to various parts of the city, with the prices from about NZ$25 and up. There is a public transport system available, but the inner city area is small enough that walking is an enjoyable alternative. Good options for inter-city travel are the bus passes and also car rental, especially if you're not traveling alone.
The Auckland hostel selection is plentiful, and you can expect to pay about NZ$20 and up for a dorm room. The city is very suitable for backpackers, as the prices are quite low, the hostel options are comprehensive, and the transport inside the city and also in-between cities is exceptionally well organized.
The sights in Auckland include the Sky Tower, which is the highest free-standing building in the whole of southern hemisphere. The adrenaline junkies can also indulge in a controlled free-fall jump from the top of the tower. Auckland has also plenty of museums and art galleries. If you're interested in fashion, Auckland is home to many interesting local designers.
Take a look at the Auckland backpacker hostel list and enjoy your stay.