My wife and I spent 10 days on the South Island at the end of May and really recommend this as a great time to go. Is it sunbathing weather, no, but, it's also not ski season. This makes it a "shoulder season" where tourist levels are low (which is nice in such a compact place) and means you can do anything you want, and most tours and experiences end up being private! The Southern Alps are capped with Snow, but, yet in valleys it is still comfortable sweatshirt weather. I could type a small anthology on what we did and where we went, but, if Queenstown, Dunedin or Milford Sound are on your radar, I'm happy to provide some of my experiences and highlights (including where to get a great pizza in Queenstown).