I applied to Pax and Strix which were closest to the school immediately after I got my letter of acceptance from KI, but it was still too late as many people already had secured accommodation in those hostels. I was then allocated to Jagargatan 20 which is 45 minutes away from the school. I would advise future exchange students to create an account on the KI housing website immediately after you have been nominated by your home university for the exchange and apply for housing. You will be more likely to get the accommodation of your choice then, as the letter of acceptance comes rather late in June.
The housing cost is a tad expensive for student housing, but considering the fact that housing in Stockholm is expensive on the whole, I guess it can't be helped. My room had a small wash basin and a cabinet and was about 3m by 3m, which is one of the smallest rooms available under KI housing. The rooms in Pax and Strix are significantly larger but the rent is only slightly more expensive than mine, so I feel the rent for Jagargatan 20 can actually be lowered to be fairer.