Llandaf used to be very quiet and mostly older residents. Slowly more families are settling there but the student residence is growing in popularity all the time so you do get quite a mix of people which gives it a slightly disjointed feel because you still have the dyed in the wool locals but there are more new faces now. There is still a sense of community but it feels diluted compared to Whitchurch, Tongwynlais or Rhiwbina. It is very busy in terms of traffic though and getting busier because of the new housing development near Pentrebane. My in laws lived there for years and DH grew up there. That being said, insole court is brilliant and we consider the Cathedral to be our family Church.
Whitchurch can feel like a through-fare because of the A470 cutting down alongside. It's funny because before I moved to the area I thought the same. I blame the big sign next to the road declaring Whitchurch Golf Club's location! But it is definitely seen as a desirable area to raise a family in. Most of the families I know are professionals in health care (consultants, GPs etc) or civil service and the adults certainly know how to keep the local restaurants, coffee shops and bars afloat.
Both primary schools are consistently oversubscribed and the only reason Glantaf isn't oversubscribed like Whitchurch High is due to the council opening Bro Ederyn in East Cardiff a couple of years ago. That situation will soon change though with only 5 spaces free in the first round of allocations this year.
Honestly though I've never encountered community spirit like the Whitchurch or Rhiwbina anywhere else in Cardiff (I've done my rounds from student digs, to single professional and now Cardiff meaning I've had a mini tour of Cardiff as a resident).
There are festivals and community events always ticking along and they are both very family friendly areas. Traffic can be busy on the main routes but most of the streets are quiet enough to cross without looking (I'm not actually recommending this!!).
I've had a look at houses with 3 beds and a garden on Rightmove in your price range and wouldn't be put off by any apart from the one on Manor Way. The houses there are lovely but they are on the dual carriageway which would put me off. You do get more house and garden for your money because of that though. North of Coryton train station is technically no longer Whitchurch but Coryton. There's a fair bit of council housing there but really the only difference is that it's closer to the M4 and further away from the facilities of the village.
There isn't anywhere I'd immediate avoid in either Whitchurch or Rhiwbina to be honest. Some parts of Whitchurch touch on Gabalfa (near college road) but it's almost gentrified those parts of Gabalfa so they don't see the issues further into the estate.
There are other lovely very family friendly areas of Cardiff too. Cyncoed, Thornhill, Lisvane, Lakeside, Heath, Birchgrove are all generally desirable and I'd struggle to think of a street that would be less attractive to live in but none are particularly convenient for the motorway. I'd avoid Roath only because it's very popular as a student/young professional area so whilst there are some lovely family homes, there are a lot of converted multiple occupancy houses.
Penarth is stunning but dreadful for commuting to the M4. The link road (A4232) is often caught up with bad traffic because of an accident/event in Cardiff Bay/game at Cardiff City football club (just been promoted to premiership so that isn't going to improve things).
Day to day I don't use the car living in Whitchurch. We can walk to the school, to the shops (including the many little coffee shops), we have access to Hailey Park which gives you a route straight onto the Taff Trail. There's also the library park at the top of the village. In terms of activities there's a very popular cycling club and tennis club and within easy reach are swimming pools and numerous sporting clubs including girls football and rugby if your DD was so inclined.
The local PACT meetings are largely taken up with inconsiderate parking near schools and busy parts of the village. Given that we're a city suburb, crime not being a large feature of a PACT meeting in any given month is encouraging.
Given the choice I'd buy one of the beautiful 5 bed detached homes in the vicinity of Heol Don with the massive gardens and make it a home for life. For now I shall be content in dwelling in my lovely 3 bed home with the sound of bird song the only noise you regularly hear.
There are Facebook community groups you could join to get a better insight to the areas too. There's a fair amount of adverts and lost pets but it does give you a feel for the kind of community and events that happen around here. I like that there's a community but it doesn't have a village mentality so your business doesn't belong to everyone.
Hope that helps a little.