Aside from all the ones listed here, many of which I don't know if I'd qualify as underrated since they show on any number of travel brochures, I found the towns of Nelson and Fairlie to be quite charming for their own reasons. Fairlie is a tiny one street town in the Mackenzie basin region surrounded by mountains and a short hop skip and a jump from Tekapo. The stars here, like all of the region, are wonderful, and there's many places to get where you won't have another soul within several kilometers of where you are.
Nelson strikes the perfect balance between a small town charming atmosphere and the conveniences and happenings of a more populated regions. It's pleasant to walk and has comfortable relaxed pubs and boutiques. It's also a short ride away from various wineries and other more well known areas (such as Kaikoura) so it makes a good launchpad to explore the region at a reasonable rate.
As others have said though, you really can't go wrong. Around every turn is a beautiful vista of some sort, and really your only complaint may be that it gets a bit sleepy sometimes or the towns begin to feel very similar. Best way is to pick some high point must sees, then connect the dots with places you've never heard of. Those mysterious dots in the middle may end up being your favorites!
Honestly, nothing in New Zealand is underrated or really that far off the beaten track. Every town there competes for visitors like nothing you've ever seen before - no matter how small the town, it seems to have an iSite (these are tourism info centers that can be as small as a kiosk and as big as a library). Residents in one town have relatives all over, and they're quick to hook each other up. The movie and TV industries also put a huge spotlight on nearly everything in New Zealand.
Don't let that discourage you. Just because other people are going there doesn't mean you won't love it. Because you will.
If you want to read up on some fun stuff, though, read "Kiwis Might Fly." It's nonfiction, and a pretty good account of many of the places, popular and otherwise.
Oamaru and Napier for interesting architecture - and Napier has a nice dark sand beach. Taupo is a very pretty town. I love Rotorua - glow worms in woods at night - bubbling things everywhere - a beautiful museum building. Nelson has great views. You can't go wrong anywhere... truly.
Fresh seafood in Kaikoura
Kaikoura is my all time favorite though (see above photo's posted by Gita), it's not just about whale watching either, you can take a great coastal train ride to get there, go diving, eat great seafood, do the relatively short peninsula walk
Akaroa is another gem, wonderful drive and great fish & chips!
"Fush 'n' Chups" & a hotdog in Akaroa
The 'Hilltop' area of Banks Peninsular on the drive to Akaroa
My NZ unsung hero is Hokitika.
I loved that little town, beautiful beach, friendly people, close to Hokitika gorge, has a glow worm dell and a perfect stopping off point between Christchurch and the glaciers or Nelson and the glaciers
Drift wood art on the beach at Hokitika
Oh one more thing, get the NZ frenzy guide books by Scott Cook. If they don't lead you off the beaten track nothing will
What Justin's said is exactly what I'd experienced, even the smallest of places has an iSite with the most friendly and helpful people on the planet, in other words, all of New Zealand seems to be Tourism-Ready. I spent almost a month in New Zealand and mostly in South Island. Two places that I hadn't read much about, but ended up spending a few days each in are Tekapo and Kaikoura. These are more like transit towns or day-trip towns where most tourists seem to walk around for a few hours and leave and not stay the night.
Tekapo didn't even have any public transport and you had to walk to get most anywhere, but that being said, there's hotels, BnBs, Restaurants and lots to do like a visit to the Mount John Observatory. Lake Tekapo is part of a UNESCO Dark Sky Reserve and it provides phenomenal stargazing opportunities. If you just want to laze around you could just sit by the beautiful Lake Tekapo or walk to the Church of the Good Shepherd
Kaikoura is a pretty little beach town where you can enjoy the most stunning clouds or do some Whale Watching or Dolphin or Albatross watching or just walk around and take in the town.Both of these places were quaint, beautiful (took the pictures with an iPhone, no filters used) and not at all crowded.