I live in Christchurch, lots to do here, including the botanic gardens (there is a new visitor Centre there and a huge free paddling pool that all ages seem to like); the museum is great; trams in the city have just opened up a figure of eight loop round the city so a great way to see it (for $20 you can hop on and off all day); the restart mall built of shipping containers, with boutique shops and lots of nice things to eat; cardboard cathedral (actually called the transitional cathedral); Antartic centre; and the gondola with amazing views over banks peninsula.
Banks peninsula is well worth a drive round, Governor's Bay has great walks and an amazing chocolate cafe called She Chocolate; Corsair is a great sheltered bay for swimming; Akaroa is lovely and you can go on a dolphin watching tour, swim with the dolphins, or go sea kayaking (I did this and it was amazing!), it is about 90 mins from Christchurch. Beaches are beautiful, Sumner is lovely, we live by the beach and there is a massive park called Broad park which has big play equipment (zip wires etc) plus a cafe and a surf club where you can swim between the flags in summer - there are free changing rooms and showers. You can hire surf boards at New Brighton or Sumner. Spencer Park is lovely and has a campsite.
One thing to consider staying in are cabins on campsites, cheap and the campsites generally have great facilities you can use including full kitchens. DOC sites are great and cheap if you have a motor home or tent. I'd recommend hiring a motor home, it is really geared up to them here, lots of places to park, and easy to sightsee.
Further afield, Hanmer Springs is great, about 90 mins from here; Tekapo is beautiful, great to do on your way down to Wanaka (which is about 5/6 hours from here); driving across the Alps via Arthurs Pass to the West Coast is stunning (NZ was made for adjectives
) and well worth doing. Picton, Havelock, Nelson are nice, we stayed at a stunning DOC campsite at Pelorus Bridge where you can swim in the river (they filmed the barrel scenes in the Hobbit there) and is right in the bush.
I disagree with the weather being like the UK, one of the reasons we love it here is that it's not! I have our winter stuff packed away and we barely use it for 2 months of the year or if we want to go up to the mountains. It can rain, but the weather is very changeable so it doesn't normally hang around for more than a day (although we did go camping one year in nelson and it rained solid for 4 days, but apparently that is very unusual). I wouldnt say it gets cold at all in summer here, but obviously the further south you get it gets cooler (although Otago is often very hot in summer) We're actually in a drought in Canterbury at the moment and it's 31 degrees today! I'd bring a light rain coat as it can be changeable, and a windproof fleece for when it gets colder (it is windy here, but generally a warm wind in summer).
Sorry that's quite long 
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