Khartoum accommodation:
Try the Youth Hostel, 35 per person (6 euros 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
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.
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. Khartoum is bloody hot (1st week of March here = 43 degrees in the shade) so definitely worth spending a little more - the Youth Hostel works out at only about $1 more 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. Walking distance to Saudi embassy, ferry companies for Aswan or Jeddah etc etc
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.
For internet I bought a Zain sim card for 5 Sudanese pounds for my smart phone, added some credit and then subscribed to their 3g internet service at 1 pound per day. Fast and easy. When I want to use it on my laptop/usb modem you can usually get them to work by dialling *99# using 'internet' as the username and password. Fast in Khartoum, fine everywhere else....
Worth the hassle of getting a 2 month visa, great people, lovely places....