Fletcher Creek is 42 kms north of Charters Towers on the road to Greenvale.
According to "Camps 5" you can stay for up to 30 days, but I noted a couple of people who appear to be permanents.
On one side of the road is a large area similar to a roadside rest area, but on the other side there is an area about a kilometre long with plenty or room to set up near the creek without being up the RRR's of the neighbours and far enough from the road for the all-night mining road-trains not to be a bother.
The creek is about 20 metres wide and a metre or so deep and flows quite strongly. Lots of kids (big and small) swimming while I was there, and they tell me there are plenty of redclaws, if thats your thing.
NOTE: There is a wooden-pole barrier about 25 metres from the creek bank and you're not supposed to camp inside the barrier, although, as some of the posts have been removed, everybody does.