The Port Hills is one of my fave places. Go to the lookout behind Sign of the Takahe, it's a nice little walk and great view, go up to Victoria Park, there is an awesome playground there and my fave dogpark in ChCh! If you're more adventurous follow the walkway from Vic park up to the SIgn of the Kiwi - we go up there quite often on the weekends.
New Brighton Pier and library.
The Groynes - has a couple of different playgrounds, an awesome dogpark again and lots of ducks - great time of year for ducklings!
And of course Hagley Park - heaps to do there and the daffodils should be almost out.
Sumner - the Scarborough walkway and through Cave Rock.
That's just a few off the top of my head