Visiting NZ via cruise ship - tramping advice

Our family of 4 were initially planning a tramping trip to NZ, then a one way cruise back to OZ. Long story but that fell through and we are now doing a 14 night cruise Sydney to Sydney in January 09. I have done a lot of tramping in NZ over the years (most of the great walks/Cascade Saddle/Young-Wilkin/Tarankai etc etc) and my preference (by far) is the alpine areas. I just want to give the rest of the family a sample of it. I'm looking for recommendations on what the best options might be for 1 day alpine type walks (or similar), taking into account we are visiting from a cruise ship and have at most 11 hours from the time of docking to the time of departure from the port. We'll be visiting Dunedin, Christchurch, Wellington, Tauranga and Auckland. I would like to fit in the Tongariro Northern Circuit which I have done before, but it is just too far away from Tauranga to do in a single day. I was thinking about Avalanche Peak near Arthurs Pass, but again probably not enough time out of Christchurch. (Bealy Spur might be an option but I don't think that walk is going to give me what I'm looking for, i.e. apline area/scenic quality) and may not be enough time even to do it. I think the options are going to be pretty thin as most of the types of walks I'm looking for are towards the west coast of the south island or the centre of the north island and just not enough time to do in a day from a cruise ship port. But any recommendations would be greatly appreciated. I've looked at options like the Mt Herbert Walkway or the Crater Rim Walkway above Lyttleton near Christchurch. By the way, which of these two walks would provide the best scenery? I've looked at Rangitoto Island near Auckland, Mt Maunganui near Tauranga etc etc, and while these may be great day hikes, I don't think it's really what I'm looking for and I'm looking at them mainly because they are close to the ports.