Avoid The Links, Smeaton, Gallatown, the area round the south side of the hospital, The Valley and Templehall.
However, where possible, go for the area round about the court (beveridge road), all the bits up Oriel Road, Raith Estate, Dunnikeir, Holly Brae, and Ravenscraig.
They'll all be available for less than my FUCKING RENT.