South Kurdufan is a war zone and travel there is strongly discouraged. Abyei is at the centre of the low-level conflict between Sudan and South Sudan, so best avoided by most travellers at this time. North Kurdufan is safer, especially in the capital, El-Obeid.
Kurdufan, or Kordofan, is a region of Sudan, southwest of Khartoum and east of Darfur.