Hellooo, sorry I have taken so long to reply. We buggered off on holiday on Boxing day, a camping trip round the South Island. Got back to quite big aftershocks and DD (2.5) not happy about it. And they are likely to keep on coming.
You are probably in the throes of packing/leaving now, so I hope I am not too late.
I wouldn't reccommend moving to the Eastern Suburbs (I would say that includes Burwood, Parklands, New Brighton, Bexley, Bromley, Aranui) as they were hit badly in the earthquakes. Having said that, where we are is an oasis of calm amongst quite a lot of liquefaction. Some of the eastern suburbs weren't actually that nice in the first place TBH.
Where is nice? Hmmmmm, depends what you are looking for. I really wanted to move to Beckenham. We first lived in St Albans, which is nice, although it did experience some liquefaction. I would do a lot of asking when renting/buying about earthquake experiences in that area, and the level of disruption. Redwood, Papanui, Harewood, Avonhead didn't seem to suffer too much, as didn't Riccarton and further out.
Rolleston is about 30k out of town and didn't suffer too much in the Feb onwards quakes. Although it was affected by the Greendale fault (Sept quake). Not sure by how much. It is quite a new development and popular.
Spend a bit of time driving around and getting a feel for the place to see what you like.
DD is quite frightened by even the little aftershocks. We stay calm (or as calm as I can be without jumping out of my skin), give her a cuddle and carry on with what we were doing. We are feeling them stronger as they are happening nearer us this time.
I hope your move goes well, and that you settle in quickly. It can be a little nerve jangling but you get used to it, and hopefully the aftershocks will die down soon. I don't know what the experience is like in Riccarton, but it does seem to be further away from the seismic action :)