New Zealand's system of Great Walks is a good indicator of quality, and the Routeburn Track is one of the most exciting of all the Great Walks. It's second only to the Milford Track in terms of popularity, and for good reason; the views and the mountain scenery over the Harris Saddle are simply stunning.
It can be a tough climb, though, especially if you're camping and having to carry the extra weight of a tent (accommodation is available but it's not that cheap and tends to full up quickly, especially in school holidays). Rest assured that it's worth the effort, assuming the weather is behaving itself, and it comes highly recommended.
As the Routeburn is a one-way track from east to west across the mountains, it can be a real pain to find transport back to the starting point at Glenorchy. However the Greenstone Track starts just before the Routeburn ends, so it's simplicity itself to tack the Greenstone onto the Routeburn to create an almost circular route. It's still not ideal, as it's 25km from the Greenstone Car Park to the beginning of the Routeburn at the Routeburn Shelter. I managed to hitch, but there's no guarantee of a lift; making friends on the walk is probably the best bet.
Together the Routeburn and Greenstone provide you with both high-level mountain hiking and low-level river valley walking, and although the Greenstone isn't up to the high standards of the Routeburn, this is a thoroughly enjoyable round trip.