If you look for a place for stay in Kilinochchi, i would say, A9 Spot is the best option you can have. Very clean and nice looking rooms. AC/ Hot water and TV. All basic needs are there. It is about 1 km before the Kilinochchi town and on your left if you coming on A9 road from Vavuniya. Driver quarters are also available.
I would highly recommend this place as a Bed and Breakfast rest.