I moved to the area about 5 years ago. Barnstaple itself is OK if nothing brilliant. The surrounding areas like Fremington and Bickington are nicer. I live in Bideford which is OK if a little backward and run down. However, the surrounding countryside is fantastic. Yes, it can be busy in the summer as others on here have noted but if you live here you can enjoy it all year round.
Not a huge number of bridleways near me so I tend to ride a mix of country lanes and old rights of way and there is of course Exmoor not too far away. Riding in this area always involves tackling lots of short nasty hills but you soon get used to that. There is always the Tarka Trail for days when you just want to ride on the flat and it is useful for getting out to the more rural areas without tackling main roads. I quite often use it to link up lots of little back lanes.
Exeter and Taunton are just over an hours drive away for work if you can beat the traffic. If you time it right it should only take about 40 minutes to get to the M5 along the link road. Once you get used to it the North Devon link road isn't too bad. Few nutters with surfboards strapped on the roofs of their cars to deal with in the summer though.