We too, prefer traveling in the shoulder/off season, and we do quite a bit of hiking.

Of the choices you've mentioned, I'd personally choose April/May (very settled weather wise or October/Nov. I'd also avoid Easter and school holidays (quite busy).

Local school holidays for 2014 can be found here:

http://www.minedu.govt.nz/theMinistry/EducationInNewZealand/SchoolTermsAndHolidays/2014SchoolTermsAndHols.aspx

March is still high season and September can still be quite cold. I'm currently planning a return visit the SI for Aug/Sept, and I'm expecting pretty much anything weather-wise.

If you're planning to walk the Milford Track, even if it's only as a day walk, you'll want to check the operating schedule for the boat that leaves from Te Anau Downs - I believe it runs through April 19 this year. Without the boat, there is no access to the track at Glade Wharf.

Walking tracks are generally open year round, but not all huts are. Bridges are often removed, which limits access during the off season in alpine areas prone to avalanches.

But don't be discouraged....there's always somewhere to walk! The options are endless.

The Queen Charlotte Track is open to bikes in the winter months, and in my experience, it's not much fun if they're on the track.

There's a mountain pass that separates the glaciers from Mt Cook. You can't go over, you must go around. There are two main routes - the West Coast (glaciers) or the inland route (Mt Cook).

If you have sufficient time, you can incorporate both, by making a loop, but the distance between the two is over seven hours of flat out driving (no stops), so not really feasible in a single day.

Most people drive from the glaciers to Wanaka or Queenstown. This can be done in a day, but do keep in mind the limited daylight outside of the summer months. There are many places to stop for photos, walks, etc, so this is still a pretty long drive day.

You have plenty of time for a leisurely trip. I suggest you make a loop from Christchurch, first heading up north, then working your way down south via the West Coast to the glaciers and Wanaka, then over to Te Anau and Milford, then to Queenstown and up the inland route via Mt Cook and Tekapo back to Christchurch.

You might even have enough time to travel as far south as the Catlins, taking in the Southern Scenic Route between Invercargill and Dunedin.

There is indeed a lot to do on the SI. I'm working on my 11th trip and still haven't run out of things to see and do.

PS - Day trips are hard to do in NZ. Queenstown makes a decent enough base to see Milford, Glenorchy, Arrowtown, Cromwell and Wanaka, but anything beyond that is quite a drive. Christchurch makes a decent base from which to see Waipara, Akarora, Rakaia, Arthur's Pass and maybe Hanmer Springs, but again, beyond that, you'd be looking at pretty long drive days.

We've found the best way to explore the SI is by making a loop of some sort.