There's heaps of stuff do to there!
Check out the view from the Botanical Gardens! Grab the cable car, and when you're getting off, go right so you're on the platform. Then before you head off into the actual gardens, you'll see a tree which is in between the most left path and one that branches right, climb up that tree and you can sit on the top because the canopy is so strong and tightly grown together.
http://maps.google.com/maps?f=q&source=s_q&hl=sv&geocode=&q=wellington,+nz&sll=59.332788,18.064488&sspn=0.541449,1.209869&ie=UTF8&hq=&hnear=Wellington,+Nya+Zeeland&ll=-41.285152,174.767828&spn=0.000779,0.001182&t=h&z=20 (the lighter green tree with a hole in the middle of it)
Go check out the seals at Owhiro Bay and the bay itself is really nice (good diving too), and while going down Ohiro Rd stop off at the wrought iron statue garden. Ask super nicely if you can check out their basement too! Wicked memorbilia down there!
Te Papa musuem, walking along the harbour. Night life, go to Alice too! Great cocktail bar! There are two enterances: one by going into Boogie Wonderland, or by going down the alley behind it, and getting in straight away.
The view from Mt. Wellington and the rope swing found there too!
Check out Sandwiches too for some good electric music. All along Cuba Street there's great places too eat and party. The Big Kumra is great on Wednesday (student nights)!
For some great Malaysian food at a great price, when walking up Cuba, between Dixon and Ghuznee St, go down the small arcade to the right and on the left hand side there's a super yummy Malaysian Place, and behind THAT there's a good Mexican place. For the Malaysian, I recommend the Rotti Shanai! I miss it ever so!
All in all, after spending about 5 months in Windy Welly, I still don't feel I know enough of the place!
I would recommend a minimum of 3 nights in Welly, and max your life :D about 8 years ago
Check this out if you are looking for things to do in Wellington:
http://nomadshostels.com/Travel-Tips/courtenay-place-a-cuba-st-best-bars-in-wellington-city about 8 years ago