If you go through Arthurs pass, Flock hill near Castle hill has lots of cool bouldering that would suit all sizes and abilities. Bring torches and explore cave stream( 45mins to 1 hr through cave. It was up to chest height so take 2 adults in case the kids need help and don't go if it's been raining or might be about to) while you are there. If you fly in or out of Christchurch this is a must do day. The access details can be found on www.mojozone.co.nz.
The Golden bay/ Takaka suggestion is good. As there is Abel tasman, rivers ocean and Climbing in at Paynes ford. Nelson Town has affordable family activities compared to most places.
Wanaka has good tramping up the Matukituki. Rob roy veiw is a great half day walk, and lots of sport climbing and you could do a Big trip staying in Aspiring hut 2 hrs up valley and the French ridge hut 5 hrs steep uphill at the base of Alpine terrain.( might be hard for the little one?)
Central North Island Tongariro area Too -The crossing is volcanic and awesome. I'd stay in the Huts with kids and make it a 3 day trip ( or longer if you do climbng days)as It's a big day. Especially if you want to Summit Ngaruahoe. CLimbing up there and at Whanganui bay/ Kinloch, etc. also lots of MTB and Cultural stuff.