Wendell
If you feel like just country driving to a really pretty spot, you could hire a car and go down to the Bay of Plenty and see Tauranga and Mt Maunganui. It's so lovely down there and is only about 3 hours or so from Auckland. You could incorporate that into a trip to Rotorua if you want to. Mt Maunganui also has fantastic natural hot springs baths and you feel like a $million after one of those - and it's dirt cheap to do.
Or (and I'm mostly jesting here) you could head to Pairoa (spelling?) and see the home of L&P softdrink, which I quite liked while I lived in Tauranga. It's short for "Lemon & Pairoa" and it's a sort of lemony tasting lemonade, if that makes sense?
Once you get to Pairoa, there's not much to do though! Basically all around there is really scenic rolling farmlands anyway, so even if you're "on the road to nowhere", it's really pretty all the same!
Where are you staying in Auckland? Ponsonby Road is a nice area in Auckland to visit - very trendy & a bit Paddington-ish. My cousin has a jewellery shop there (Shell Shock), so if you go in there, she might be able to give you some tips. Just ask for the owner, Merete. If you want to PM me, I'll be happy to give you her phone no if you want to give her a bell and ask for suggestions.
Don't knock Auckland too much. I really like it, especially if you have a car to drive around in for a day. The other 2 days, I would get out into the countryside. NZ is fantastic, I absolutely love the whole place!
Also in Auckland is a really tall tower - forgotten the name - but it has a good restaurant (apparently) with superb views and an external glass walkway around the top that you can freak out over. Just a thought.
Enjoy your stay.