Exmoor - the waters mentioned by Gudgeon are worth a look (half of Exmoor and all of the Dulverton waters are in Somerset but they are no worse for that!) If you are in the area the Lyn on the north coast of Exmoor is a must do.
Going west into north Devon there are good hotel waters for trout on the Taw (Fox and Hounds, Eggesford) and Torridge (Half Moon, Sheepwash). Both of these also have a reasonable chance of salmon/sea trout given the right conditions...
Dartmoor - the Duchy ticket gives access to miles and miles of the East and West Darts plus several useful little tribs. The Upper Teign FA have, not surprisingly, most of the upper Teign. I've always found the trout fishing a bit uninspiring on the upper Teign but that might just be me. Lower Teign FA and Dart AA waters (on the lower Dart) I always think of more as salmon/sea trout fishing and have no first hand knowledge of the trout fishing there.
The Avon (Devon) has some nice trout water and it is closer to the south devon beaches than the other Dartmoor waters. On the western edge of Dartmoor the Tavy, Walkham and Plym club has a lot of water.
The Westcountry Angling Passport (Previously Angling 2000) has water all over Devon and Cornwall. I have been told that it also covers the Duchy water on Dartmoor now but can find no mention of that in the web site.
All of the above can be found in
Get Hooked | Get Hooked Guide to fishing in Cornwall, Devon, Somerset, Dorset, Wiltshire, Hampshire, South Gloucestershire if a google doesn't find them.
Andy