We live in Whitchurch, and I highly recommend it. The area on and around Heol Don and Church Road, just north of Llandaf station, is especially good, with some lovely period houses for less than you'd pay in other areas like Pontcanna.
If you drive then you'll appreciate the ease of getting out of the city -
either to commute on the M4 (this is what swung it for us, to be honest) or to get up to the Brecon Beacons on the A470 at the weekend. Parking is a heck of a lot easier than in many parts of the city; many houses have driveways, which obviously helps!
Public transport is good - there are buses into the city every few minutes, and trains from either Coryton or Llandaf stations. The latter has the better service, with trains every 10 minutes taking less than 10 minutes to reach the city centre.
There are good nurseries and schools to cover both English and Welsh medium (e.g. Acorns and Si Lwli for nurseries, Whitchurch Primary and Melin Gruffydd for primaries, Whitchurch High and Glantaf for seondaries) all within walking distance.
There are plenty of other facilities - library, churches, community centre, dance classes, scout hall, and a small but lovely park all spring to mind. The high street is great, and has an unusually wide range of options for food shopping (from Iceland to Co-op to a great independent greengrocers to two fab independent butchers), cafés (from the greasy spoon to the chic options!), banks, hardware, "lifestyle accessories", greetings cards and most other things you need locally.
There's also the Forest Farm nature reserve down by the Taff, where you'll also find the Taff Trail which is a great cycling/walking route into the city, down to Cardiff Bay or north into the hills.