There are several options regarding accommodation in Minsk.
This year we launched our "getting accommodated initiative", where you can stay with an Belarusian attendee.
If you want to be more kind to your budget, we also highly recommend the Trinity & Riverside Hostels. These are two small but cozy hostels by the same company in the historic part of the city. Bed prices start at € 8 in a 6-bed room. A room for two will cost € 23 (two separate beds) and € 27 (double bed). They have recently added nice breakfasts for only € 1.8.