When we stayed in Cairns it was at a small family run B&B and it turned out to be really brilliant. Their website is http://www.galvinsonedge.com.au/
and I can highly recommend it. It can sleep up to four people because there are 2 bedrroms, 1 double and 1 twin. You have a bathroom, small kitchen and living room. You can walk straight out onto a patio/garden area where there is a swimming pool. The price you pay is for the whole place regardless of if you are a single person or a family of four.
Julie and Jesse really do look after you and there is always plenty to eat at breakfast time. You couldn't want a friendly place to stay and Julie will help you if you need any advice booking any trips/car hire etc. If anyone has any questions which you can't get the answers to from their website, either email them or ask me.