Here's my cheap and free list for Auckland:
General tip: It is not customary to tip in NZ, and locals usually don't bother.
Transport cheapies and freebies: Free city circuit bus - No scams or catches, just a free bus funded by the city to let tourists get around. The bus is the only one which is bright red, and runs every 10 minutes, every day of the week between 8am and 6pm. Map of the circuit is here:
http://www.stagecoach.co.nz/citycircuit/index.htmlFree bicycle tuk tuks - red again, just flag them down and tell them where you want to go within the cbd.
Cheap CBD bus fares - if you are travelling a short distance on the bus within the CBD, check with the driver to see if you can get a 50c fare, instead of paying for a whole stage.
If you're doing a lot of travelling in one day (probably includig a ferry trip) you might want to look at the day pass from
http://www.maxx.com. Check out the journey planner there too.
Transport tip: I would recommend taking the bus over the train wherever possible if you need to ensure you arrive at your destination on time...
Sights to see and places to visit: Skytower - rather expensive to take the trip to the top ($20ish NZ) and in my opinion not really worth it unless you really do have the cash to spare. If you choose not to go up, the tower looks pretty good from the ground, and it's free! Go at night when it's all lit up (different colours for different occasions) or go in the daytime and watch crazy harnessed tourists jumping down towards you.
There is an information centre inside the building next to the tower, and the long distance bus departs from here too. There are also a number of restaurants/bars inside - the main one on the ground floor (called Rebo) does some basic flat pizza breads as starters which are pretty cheap ($5 - $7 NZ) and do fill you up - don't feel bad about not ordering mains, they won't mind.
If you hire a car and want to drive into the city, park underneath the sky tower, take the lift up to the casino and validate your ticket (for free) at the machine next to the lift for cheaper parking right in the centre of Auckland.
K' Road - Short for Karangahape Road, this is probably the most famous street in NZ. Eclectic shops including tonnes of second hand and vintage clothing, a truly interesting set of people live, work and socialise here. You don't need to buy anything to enjoy the experience, but there are some cheap bargains to be had. There are a number of gay and lesbian bars in the central portion of this long street, and as you work your way away from the CBD end there are a few sex shops. Not at all dodgy in the day, slightly dodgy at night but nothing compared to other cities of the world.
Auckland Museum - special exhibitions can be pricey, but you can visit the War Memorial Museum for free, and the rest of the permanent exhibitions for a donation of your choice (suggested is $5 NZ pp). For $15 NZ you can see A Maori Cultural Performance, which includes your donation to see the rest of the museum. If you are heading to Rotorua later in your trip, you may want to skip this, as Rotorua is really the home of Maori Culture and you will likely see a performance there at one of the attractions you'll visit.
http://www.aucklandmuseum.co.nz Mt. Eden - the highest (dormant) volcano in Auckland just outside the CBD, one of the now most pricey suburbs now has been built on the surrounding land. Take a bus from the CBD for about $2 NZ. There are cows and sheep grazing freely on the hillside, and once you reach the top you'll get a great view of the whole city, including the numerous other volcanic peaks. Work up a thirst on the way down and 10 mins away is the Mt Eden Village where you can grab a beer if you like (pricey at about $6nz). Take a wind jacket or something to keep you warm.
Auckland Viaduct Basin - This is a bar, restaurant (and pub/club in the evenings) mecca, built for the America's Cup boom a few years ago, but still popular with city workers for flash lunches and after work drinks. Again, a great place to people watch, and you can check out the KZ1 Yacht, the actual 1988 America's Cup Challenger Yacht from NZ suspended right there above the bars and the Maritime Museum. This was the yacht that made Dennis Connor decide to build Stars and Stripes.
Devonport - Take the ferry from the waterfront of the city ($9 NZ return pp) and get a great view of the CBD and our Harbour bridge as you leave. Devonport is another volcanic site, popular for its small cluster of shops which include an eclectic mix of artisans, booksellers, restaurants, cafes and art galleries - no need to buy anything, you can spend all day just looking around. You can walk quite far up and down the beach, or relax in the park a few metres back.
Mission Bay - nice beach suburb, very popular during summer. A nice mix of restaurants and takeaway joints where you can get a Burger (fancy, about $7 per burger), Pizza (about $14 per pizza),the classic kiwi tradition Fish and Chips (about $7 per person for a good feed - try the paua fritters!) or take your own picnic dinner and sit on the beach overlooking Rangitoto island. Great for people watching as lots of first dates seem to take place here. During Dec-Feb there are sometimes free Salsa dancing lessons on sunny weekend afternoons.
If you're here during summer, check out
http://www.aucklandcity.govt.nz for free concerts and other events.