Akaroa is lovely - you can do one of several cruises on the harbour, and if you have someone to leave the kids with you could also do dolphin swimming (with Hector's dolphins - smallest in the world). There are also penguin tours out that way, some of which you can kayak to.
Plenty of small cafes and galleries to look at, and the Giant's House (art house, with amazing mosaics) is worth a look. Wineries and cheese factory also.
Christchurch (where I live!
) is somewhere you'll be going through. With the kids so young I recommend visiting Willowbank wildlife park and the gondola is also interesting. Not sure if the tram will be up and running by then (probably not - much of the inner city area is still shut down due to demolitions from the earthquakes).
If you're wanting to head somewhere else with the kids for a few days, my personal favourite is the Abel Tasman region. Just stunning!
You could also go to the West Coast if you wanted - the glaciers are great (I went there when my kids were aged 3 and 1 - we were able to do the small walks, not the long hikes to the glacier though) and places like Punakaiki are also cool. Again, with kids the age yours will be, your best bet is to just find somewhere with a simple playground.
Let me know if you want some more specific info - I've travelled all over and live here.