Accommodation in Canberra can be expensive and especially camping options are very limited.
The better option (and the recommended one) is the Alivio Tourist Park. Early bookings or joining their "alivioadvantage" program online at aliviogroup.com.au will get you the best rate or try the online booking services. Also the bigger the number of people in a group, the cheaper the price per night in their cabins.
If you are looking for B&B or other options the Canberra suburbs of O'Connor, Lyneham, and Dickson will be close to the action.
The closest camping options are at exhibition park http://www.exhibitionparkincanberra.com/camping/