We lived there when the kids were little (pre-school). It's okay. Better than Thornton Heath. Not as good as Streatham/Norwood. What you would expect really given it's relative affordability. It's kind of a nowhere-y place in terms of identity, somewhere you drive through going in or out of London. It didn't really feel like a place 'to come from' if that makes sense, in terms of how our kids would have come from there, which is an abstract kind of thing but having grown up outside of London in a place with a proper identity, it felt like a strange thing that was missing. Even in Thornton Heath, the grimness gives you something to react against and hence it's got the music culture. Norbury is more neutral.
That said, it has the basics - okay shops, a couple of parks, small library, gym, only one pub that I can think of (not much of a drinking culture because of the Asian community I assume), there are some schools black holes to be avoided but some of the primaries are okay and there's a girls secondary. Decent train service. Mostly safe feeling walking back from the station at night.
Fundamentally it's fine and we were a bit torn about staying there in affordable home or stretching more to move somewhere better with more going on. We opted for the latter with no regrets, but still pop back there occasionally to the park or the dentist. There's plenty of dentists!
So worth a look for sure, but maybe suss out South Norwood and some of the other Croydon suburbs to see where suits your needs/budget best. One thing I did like is that Norbury still has a London postcode, but you might find some of the places further out have a nicer family feel.