Well in that case I would say look at the areas to the South of Christchurch, huose prices are reasonable and you are easily on the road to Castlehill.
I would think twice about bringing your bikes with you though, unless you have something really special, it probably is not worth the hassle or expense. I can say this because we brought our two SV650SKs out with us and have hardly ridden them since we got here and are planning on selling them next spring. The reason for this is that although the scenery here is fantastic, the roads for biking are pretty boring. Most are straight for miles and miles, then there are those straight gravel roads which I won't touch with a road bike, then if you want to go to the mountains, unless you are going touring you have to come back the same way you went. We are thinking of either getting a quad bike or a small off road bike
Lincoln is a nice town about 15 mins from chch
in fact if you don't want chch itself then all the area shown in this map would suit
Multimap - Maps
You can spot the less nice areas in chch as they are the ones with grafitti and loads of advertising posters stuck to fences.
Be aware that most peope living in chch will not understand a UK persons willingness to commute, it just is beyond their understanding, they will also tend to rubbish the smaller towns around as being backwaters, so take those sort of comments with a pinch of salt