As Shortea says you can get a ticket for the EA stretch on bottom 3 miles or so of the Lyn from the tourist info in Lynton town hall. It's all good but the water upstream of Watersmeet has less walkers although with a bit of scrambling you can find seclusion on the lower section. All of the EA ticket water is in a deep wooded valley/gorge with many small falls and deep pools. There is also another day ticket stretch up above Malmsmead which is very pretty and a bit more open in places.
For some open moorland water the Exmoor Forest Hotel at Simonsbath lets day tickets on the Barle above Landacre.
If you want more detail drop me a PM
Cheers
Andy