There did not seem to be a whole lot of options in Jaffna for budget accommodation but we stayed here based on a friend's recommendation. The staff was very friendly and they had lots of pets! We played with a very, very cute 2 month old Dachshund. I think our room (double) was less than 2000 rupees and had its own private bathroom.
The only thing is we wished there was a mosquito net as mosquitos were a problem. Also remember that this will be a bit removed from 'downtown' and to our surprise, there aren't really any restaurants in the immediate area!
Nonetheless, this is a fine place to stay and the staff will help you get to wherever you want in Jaffna.