Having been born and bred in Exeter, I ought to know some routes, but on reflection I never really cycled very far outside of the city as a kid, and left the City at eighteen to go to University, never to return, aside from visiting family, but I normally drive there, so little cycling.
The best suggestion I can think of is cycling from Exeter down the west side of the Exe, following the route of Brunel's Atmospheric Railway. If you keep as close to the coast as possible, you'll avoid some of the busier roads, which is not to say you won't get traffic, although it won't be as bad this time of year as it gets in the summer holiday times. I would imagine you could also follow the Canal at the Exeter end of the route, someone out there should have planned a route along some of this, but I haven't managed to Google one out yet.
(If nothing else, it's worth Googling for details of the Atmospheric Railway, which was an awesome if somewhat ill fated idea).
Personally I'd avoid cycling across Dartmoor, since it's stupidly hilly, but if you like hills, it would be an interesting route to go. Certainly very scenic, and lots of nice Tors.
