If your budget is approx 200k then I'd like to stick in a positive word for Catford. I've lived on SE6/SE13 borders since 2002. I'm a woman (5 foot 2 and white if that's relevant) and I've never felt unsafe walking locally after dark; I often pop out for a pint of milk from the 24 hr shop in the wee small hours [insomnia is a bitch]. Your budget should get you a really decently sized one bedroom (with maybe titchy second bedroom) flat with garden on Mount Pleasant, Radford, Theodore, George Lane. Keep an eye out also for properties on the triangle of Rushey Green, Wildfell and Albacore. It's not an exciting area to live but in the ten years plus I've lived here every move has been positive. We have some really nice pub/restaurants now. We didn't have them 10 years ago. And it's within a short, single bus journey to Greenwich, Blackheath and East Dulwich. We have lovely parks. There is a real sense of community here. My mum loves it (and she lives in Holmes Chapel). Good, if not perfect, transport links to central London. Rushey Green/Davenport/Ringstead are also good places to look.