Hi there I live in Ilfracombe and its tough to find public paths belive it or not, I head up the Tors staying high and down through Lee woods and back for a quick burst or over to Croyde around baggy point via the Tors and Woolacombe for a mid size ride Pubs are grampus in Lee, Red barn in Woolacombe and for the best Cream Tea or cake the sandleigh tea rooms at croyde side of Baggy .
As for Lymmouth get there early for free parking and to avoid the miserable walkers all telling you its a footpath as they did today and head to watersmeet then to Brendon/ East Lyn river. Its some of the best scenery in England, also Horner woods in Porlock and Simmonsbath to Tarr steps Dulverton in is amazing riding but i would avoid the higher exposed ground at the moment as its very boogy at the moment.
The coast path is short down hills, hike a bike up hills and not great for long ride stretchs, hope this helps and you enjoy your stay here its a great part of the world. If you need any more help just ask
Matt