Excellent mountain biking in NZ. Usually in forests, but depends where you are. Purpose built, mountain bike only trails in Rotorua, Taupo, Kawerau and Auckland (35mins from the city) to name a few. Good bikes can be hired from many bike shops, plus there are organised trips/guides etc.
It is a small country, but quite a big place to get around, if you know what I mean, so with 12 days you do not want to do too much travelling, so as you are arriving in Christchurch, I suggest you spend most/all your time in the South Island. Very beautiful place. Plus as stated above, you can get all the adventure stuff, plus vineyards (Malborough), mountains, world heritage park (Fiordland), glaciers (Fox and Franz Joesph) West coast sth island.
You could fly up to Rotorua, interesting place if you like geothermal activity.
Have fun, I would rather be there than sitting here in Bangkok, but that is what happens when you are a refugee, economic refugee that is
cheers
Neil
90C4 (in NZ)