Come to one of the Croydon suburbs. Shirley, South Croydon or Purley. You should be able to get a 2 bedroom property for around �850 pcm.
There are trains, every 10 minutes at peak times from East Croydon to London Victoria taking15 minutes. There's also many bus routes throughout the area, including a direct, non stop bus from West Croydon bus station to Waterloo. We have Trams too.
I've lived in the Borough for about six months and have worked here for 3 years. It has it's good and bad points, Chavish areas like New Addington and good points like a pretty good shopping centre in the centre. I've not really experienced any nasty episodes.
If you go to the Croydon council website www.croydon.gov.uk (Check Sutton council too, as some areas come under that borough) you can see the various Council tax bandings and costs. I would definitely recommend the London Borough of Croydon.