Parnell Rose Gardens

AKA the Dove Meyer Robinson Park...probably not worth the trip there on its own but if you are going to be in the area it is more than worth it.  As you would expect there is a nice rose garden as well as a collection of other small gardens, flowers, impressive trees, monument to the Korean War, short walks and ponds.  There is a car park next to the rose gardens which is a popular place to park up and look out over the Ports of Auckland to the Harbour and beyond or if you walk up the steps there are some nice seats to enjoy the view.  Most people parking here are usually eating takeaways which seems to have resulted in a resident population of wild cats/kittens (better than rats I guess).  The park also borders a nice lagoon and the Parnell Baths (swimming complex)

Albert Park

A nice park in the central city on the site of an old militarry barracks established in the 1880s (part of the wall is still visible in the university) with beautiful trees, flowers and grassy areas.  It is adjacent to the stunning University of Auckland grounds so during summer there are plenty of students lying under the trees napping reading or cuddling.  There is a Victorian fountain, a band rotunda, massive trees with amazing roots and trunks, statues of various figures important to New Zealand, war memorial and old artillery guns.

Auckland Domain and Winter Garden Pavillion

Right in the middle of the city and surrounding the Auckland War Memorial museum (see my other post) this is a real gem. You can easily walk their from central Auckland and while it does involve some steep hills the route from the city has a a few sweet bush walks. The area is popular with joggers and fitness walkers and there are numerous grass playing fields for impromptu games of soccer or cricket. Next to the museum is the Winter Garden Pavilion which has indoor and outdoor gardens as well as a large fountain with an ice cream shop, duck pond and toilets nearby. The best place for a picnic or lie down is the gently sloping grass in front of the museum which has great views of the ports and harbour. The area is very spacious with plenty of sculptures and there are also regular concerts like Christmas In The Park and Starlight Symphony.

Music Point

A great place for a weekend stroll.  You can park at the beginning of the golf course and walk all the way or drive right to the driveway entrance to the radio station building.  Plenty of grassy Knolls, views of the Hauraki Gulf and its islands, shade from trees, picnic and photo spots.  And to cap it all off there is also a historic building with history.   There is a steep walkway at the tip of the point to get down to the shoreline and at low tide you can explore the rock pools, cave and island/rock.  Look out for Tui's in the trees and bunny rabbits in spring...oh and golf balls lol. 
http://www.welcome2manukau.co.nz/tourism/product/?product=musick-point

Auckland Botanical Gardens

While it is not the most beatuful or exotic public garden it is very expansive and diverse for the middle of a sprawling urban city.  It encompasses numersous themes and backs onto an area of bush providing plenty of short bush walks.  One side of the garden is spoiled by traffic noise from the adjacent Southern Motorway but it is so big that you can easily get away from this.  Perfect for families or a lovers stroll and you could easily spend a few hours here. 
http://www.aucklandbotanicgardens.co.nz/