NZ North island DIY post cruise ideas?

I'm in the planning stages for a solo transpacific cruise that ends in Auckland, and I'd like to spend a week in NZ afterwards (can't afford to spend more than a week, sadly). Typically I'm more of a DIY traveler than a person who likes excursions and tours, but it's a part of the world I've never been to.......I'm thinking about renting a car and tooling around the north island for a bit, ending again in Auckland for a flight home.

Any suggestions of places/sites/routes that you'd recommend? I'm not interested in Middle Earth/LotR sites though. My preferences lean towards culture/history/art/scenic, and nothing more strenuous than a beach walk or a light hike.

We spent three days prior to our cruise in the Bay of Islands. We went to the Hole in the Rock but did not have time for the Treaty Lands which are supposed to be quite informative. We also did a day tour to 99mile beach. We had to do a tour as you are not permitted in a rental car to drive on the beach. It was great. We stayed in Russell at a lovely b and b. Getting to the northern part of the North Island requires you to pay the $2 toll online. It was quite confusing. We bypassed the toll road on the way up as we couldn't figure it out. Had not recovered from the 20 hour flight from the US. On the way back to Auckland the owner of the b and b paid for it and we paid her. She knew how to maneuver the payment. We only spent one night in Auckland but there is quite a bit to see there as well. You could spend a lot of time on the North Island--quite lovely. Enjoy. We were there the end of January if that matters.

Pearl

Check out the The Twin Coast Discovery Route...

http://www.northlandnz.com/images/uploads/pdf/northland_printable_map_2012.pdf

If you enjoy wine, there are some great vineyards near Auckland that have tasting rooms with some having a restaurant.

Try to see the West side of the North Island around Auckland. A lovely, wild-type view of the coast, I thought.

Thanks for your ideas and input; I have a lot of research to do.

As a solo traveler, it might be cheapest for you to join a nice bus tour. We looked at them but with 3 travelers in our party and the fiords cruise stretching the budget a bit we are doing a self drive tip. ATT Kings seem to do many of the tours with medium to upper rooms. My friend did 19 day bus tour and had a grand time (though I would not want nor could I stand that long a bus trip).

Go to the 100% New Zealand tourist site (I google "100 New Zealand" and it comes up) I-site for government sponsored tourism information. Lots to see there. Check the bus tours. If you don't want to do a bus tour, it is a fast and easy way to determine what to see and do. Their itinerary on the bus forms an outline for independent traveler. Can also do a bus pass that allows you to go town to town. Our basic itinerary came from a Qantas airlines vacation travel brochure that we picked up from a travel show this spring. Check out trip advisor New Zealand forum boards and there are many many itineraries there and people are very kind to give advice and tell you how long the drives are on NZ roads.

So dive in and start looking. See what you want to see. A day's drive or a two day bus trip brings you up to the Bay of Islands (Pahia) area and then on to the Rotorua area for thermal features and native culture. Auckland itself has many sights and could be your base for day or two day trips out.