The problem really is your base. Exmouth, being bordered by the estuary, limits you to repeating the first part of most routes. You could head East but that would miss some good routes and views peculiar to South Devon and the Moor.
Here are two routes that I can recommend:
Leave Exmouth on the main road for Exeter.
After Ebford, turn left for Topsham.
Continue through Topsham to Countesswear Roundabout and turn left (first exit).
Cross the Exe estuary via Pegasus Bridge, at the next roundabout, turn left (first exit) onto the A379.
Stay on the A379 through Kenton, Dawlish and Teignmouth. Follow signs for Kingsteignton and Newton Abbot.
Through Newton Abbot and pick-up the A381 to Totnes.
At Totnes, remain on A381, follow the signs for Kingsbridge and at Halwell, turn left onto the A3122 for Dartmouth.
You could stop here for lunch.
From Dartmouth, A379 (again) for Stoke Fleming, Blackpool Sands, Strete, Slapton Lay (good place to stop and take-in the events of Operation Tiger - Google may help) to Torcross.
Remain on the A379 to Kingsbridge via Chillington, Frogmore, East and West Charelton.
From Kingsbridge, B3194 & B3196 via Loddiswell to Wrangaton.
At Wrangaton, turn right onto the A38 and a quick blast up to the M5, leave at junction 30, then a short ride back to Exeter.
Distance is about 130 miles. Plenty of coastal roads until Torcross. After that nice views across the South Hams to the southern edge of Dartmoor.
Alternatively:
Main road from Exmouth to M5 Junction 30.
M5 South, a short hop to Junction 31 then follow signs for Okehampton.
A30, again short hop to the first exit (Exeter, Alphington).
Take the minor road, first exit (left) and follow the signs for Moretonhampstead (B3212 via Longdown).
Through Moretonhampstead, via Postbridge (the pub there does nice Devon Cream teas) to Two Bridges.
At the T-Junction turn left onto the B3357 to Ashburton via Poundsgate. From Ashburton follow signs to Buckfastleigh.
At Buckfastleigh follow the A384 for Totnes and from there reverse the first route back to Exmouth.
This second route will give you all the same coast roads but begin with some lovely Dartmoor roads (particularly through Poundsgate).
It would be my preferred choice. In the good old days, I used get paid to ride around such routes.
