I was just looking at the Heaphy Track when I was checking out the Nelson area on google maps. Wish I had made the effort to get on that track while I was at university outside of Christchurch for a year. This was 35 years ago -- it might have been a bit rougher back then, but I was tougher myself back then...LOL! I did get on part of the Routeburn track mid-winter on a solo trip. And made several tramps into the Southern Alps, but that's too far south of Nelson!. If you do happen to get that far south, I have taken several day-hikes out of Authur's Pass -- pretty steep (esp with a 4x5) but great once you are up there!
And several years later I tramped a big loop in Abel Tasman National Park -- hiking on incredible beaches heading north on the Coastal Track...feasting on shellfish. And returning on the Inland Track through the mountains (out of food except for flour...not very interesting fare. I found out that night why the hut I was in was tied down by cables from all four corners! Great view of the coast from a bit over 2000 feet, but did the wind hit the place! That was a 7 or 8 day tramp.
Several years later (again) I did some tramping up in the Nelson Lakes (with a 4x5) -- very beautiful -- up to Lake Angelus. But given only a month and seeing as you probably have seen alpine country before, I would suggest exploring closer to Nelson and out to Westport (on the west coast, of course), but what the heck, it is less than a couple hours away! There are some old coal mining areas north of Westport if you are into that sort of thing...and a seal colony just to the south.
Make friends with someone with a boat -- now that would be the way to see the area! Depending on National Park regulations, it would be great to be dropped off by boat at a hut along the Abel Tasman Coastal Track, with food and camera. Spend a few days and hike out.
Vaughn
PS...sorry for the wandering post -- tripping down memory lane!