We used to live in Crofton Park and are still nearby. It's changed out of all recognition since we first went there, well over 35 years ago.
It's a very green, leafy area. Terrific parks: Blythe Hill Fields, One Tree Hill, Hilly Fields, Telegraph Hill and Ladywell Fields. Several interesting little community gardens and nature reserves dotted about. Lots of cemeteries in the area which are gradually also turning into nature reserves as they are not much used for new burials these days. Lots of street trees.
Transport: the train service from Crofton Park is much improved. Those trains go to Blackfriars with an easy change onto the Circle and District lines and to Thameslink services going north through Kings Cross.
It's also easy walking distance to Honor Park and Brockley stations, which are on the same line, changed out of all recognition from decades ago. The main line service goes from Sutton to London Bridge and the Overground goes from West Croydon to Highbury and Islington, so it's four stops from Brockley to Canada Water where you can change onto the Jubilee Line.
Slightly further afield there are Lewisham, Ladywell, St John's and New Cross stations and there are also several bus services, so there are lots of travel options when the obvious ones have problems.
Other things: lots of coffee shops these days. Various pubs and wine bars. A few places to eat in. Some good takeaways, e.g. Brockley's Rock. The Babur (Indian) restaurant is absolutely excellent. Le Querce used to be a very good Italian restaurant. Haven't been there for a while so I hope it's still thriving.
There's a good interesting independent bookshop in Brockley now. Volunteer-run library in Crofton Park. Full library service in Lewisham.
Brockley Market every Saturday in the car park of Lewisham College (Lewisham Way). Farmer's Market in Telegraph Hill.
Lots of chain shops and supermarkets in Lewisham, which is very nearby.
We find it a very safe area.
State schools are good, from nursery through to sixth form. Lots of good independent schools in the area too. Grammar schools in outer London are reachable by train if that's an option from 11.