As posted elsewhere:
Try the Youth Hostel, 35 per person (5 to 6 euros per person if you choose a good 'bank' to change money at) for shared rooms, great location, secured shaded parking under a huge mango tree with a sweet old guardian, clean and well run, air con and fans. Even a working fridge in each room and a shared kitchen to use. Loads of good restaurants etc around.
CAMPING IS POSSIBLE for 1.5 Euros per person (10SP), some shade, can sit in the air con reception area, wifi (sometimes!) etc, clean facilities and electricity for the car.
Rooms have between 2-6 beds in them, I am sharing a 3 bed room with my 'wife', so we effectively end up with our own room for a decent price. Foreigners get there own room, so if your the only foreigner, which seems normal, you get your own air con room for 5-6 Euros, a real bargain in expensive Khartoum.
Walking distance to the airport. Walking distance to Saudi embassy, ferry companies for Aswan or Jeddah etc etc. Next to the Dutch embassy as well ;-)
GPS N15 35.478 E32 32.386 (Only Landies and Toyotas will fit through the gate/trees - trucks will not fit!)
Sudanese Youth Hostels Association
We tried camping at the 'National Camping Residence' which is nice, clean toilets and showers, but hardly any shade and its a long walk to anywhere being right on the edge of town, a 13km drive to anywhere. Khartoum is bloody hot (1st week of March here = 43 degrees in the shade) so definitely worth spending a little more - a room for two at the Youth Hostel works out cheaper than camping at the Blue Nile (constant bad reviews).
If no suitable rooms are available couples may have to sleep in separate rooms as it is strictly separated by sex per room etc
Worth a try, I'm enjoying the electricity for my laptop, cold fridge, pizza from the Deli next door and the gentle hum of aircon after a hot day of mechanics.
Having looked at all of the Khartoum options in my combined 2.5 weeks here, I seriously recommend the Youth Hostel, a really great place for the money.