If you are bringing your family with you to Durham, you can look for properties on student accommodation websites, but it is important to be aware that these sites are often designed for single students looking for shared accommodation with other students, so there may be a limited number of properties which are appropriate. Some sites will allows landlords to specify on their advert who their property is suitable for, and some properties are advertised as suitable for couples, families and/or staff members. It may be worthwhile to contact "professional" (ie non-student) estate agents in Durham as well.
Please note: if there is a mix of students and non-students in a property, the property will remain liable for council tax. The non-students will be liable for the total bill and the students at that address will need to obtain council tax exemption certificates from the University.
College accommodation within the University for families is very limited so most students bringing children or partners with them live in private accommodation. Please see here or contact the Accommodation and Allocations Office for more information about college accommodation for couples and families. University-managed family accommodation is offered by Ustinov College.