I grew up in Croydon and lived there till I was 37 (1996). We still go back regularly, as DP's mum still lives there, as do some of our friends.
The further south you go, the nicer (or less grim!) it gets. There are undoubtedly areas that are high crime and I would check out the local crime mapping thingy before making any firm decisions.
Even in the nice areas, you can get a lot of anti-social behaviour if you happen to live close to shopping areas where there are lots of bars.
Transport links are great, but traffic is dreadful. You can be a long way from a main road, but still hear constant traffic hum, but I guess that doesn't bother everyone (it drives me mad - I hate it).
I also think that it's changing. DP's BIL still does a lot of work up there, and told us recently that Norbury, which used to be pretty rough, is now getting gentrified and full of trendy shops, "nice" coffee shops and ladies who lunch.
If Norbury is going up in the world, Thornton Heath may not be far behind! And we've also noticed that areas further out, like Purley and Whyteleafe, seem rather more shabby than they used to.
@DSHathawayGivesMeFannyGallops I'm guessing you mean Selsdon, and if so, my old school was built in the grounds of the hotel you refer to! The hotel's outdoor swimming pool was a popular venue for small hours skinny dipping among my crowd, and I misspent a large chunk of my youth in the bus shelter by the traffic lights.