Durham has a Premier Inn which is well located for both social events and debate venues. The rooms can be for up to 2 people, with prices for the duration of the conference as low as £93 per delegate (as checked on 28/06/18). The organisers will not be assisting with this, and delegates will have to book through the hotel website.
Otherwise, other plausible accommodation options include Marriott Hotel which is a 5 minute walk away from Elvet Riverside, the various AirBnB locations available in the city, or even accommodation in Newcastle which is only a 15 minute train journey away from Durham.
Durham University Model United Nations 