I lived in Auckland from July '08 until June '13, there's skate parks scattered all over the place. I lived near Manukau, so I had the Heyman Park one to myself a lot, the first 2 years. There's a few weird ones, and by weird I mean, the super steep BMX style transitions, but still there's a lot of diamonds in the rough. The best one is downtown, Victoria Park. Here's 3 links to my fave ones:
http://www.skateparkhunter.com/new-zealand/manukau-skatepark/http://www.skateparkhunter.com/new-zealand/newlynn-bowl/http://www.skateparkhunter.com/new-zealand/victoria-skatepark/Record shop, THE place to go is Real Groovy on Queen Street, I got heaps of great vinyl there, which I brought back of course.
http://www.realgroovy.co.nz/As far as touristy style attractions, make sure to visit the Domain downtown, cool park with a NZ history museum at the top of the hill. Museums costs a $10 "Donation" (I dunno why they don't just say it's a fee), and it's awesome. Lots of great info/sights in there. Make sure you go to One Tree Hill, great views of Auckland, I took a lot of pics there. Museum of transport and so forth:
http://www.motat.org.nz/The skate shops kinda went weird while I was there, but there was one TINY one downtown, at the top of Queen street I believe. "Cheapskates" is the standard shop. There's a shop called Wrongskate (they have a skatepark as well) and those guys were super cool and nice.
Also, a few hour drive away, but make sure to go to Tauranga. Super mellow vibed place and awesome scenery. General vibe I got from the people there was pretty chilled and they like to have fun and party. There's obviously great scenery everywhere you look. Muriwai beach has some of that black sand. There's a few of those beaches around, got some pics there as well.
There's a million clubs downtown, all sorts of venues. I myself am heavily into hardcore/metal etc so the ones I knew the best were the King's Arms, and the Powerstation. King's Arms is a nice small place though. Dunno what kind of music you're into but my friend/tattoo artist is the drummer of a devilish blues band called His Master's Voice and they're pretty cool. Lots of original music there, that should get more notice than it does. Hope this helps!