Dartmouth
Famous for the Royal Naval College, Dartmouth is a beautiful town on the estuary of the River Dart. Walk out to Dartmouth Castle (or you can take the ferry) or just browse around the local shops. There are some excellent (if expensive) restaurants. Walk to Bayards Cove and have a drink in the Dartmouth Arms or try the Cherub pub at little further up the hill.
From Dartmouth you can take a variety of boat trips up the River Dart ranging from a one hour non-landing cruise to a full trip up the full length of the navigable estuary to Totnes. You can also get a ferry to Dittisham (the locals pronounce it Dit’sum) where you can visit Greenway House or have lunch in the Ferry Boat Inn pub.
Many visitors take the “Round-Robin” package offered by the ferry companies which combines a train ride on the Dartmouth Steam Railway from Paignton to Dartmouth, a river cruise from Dartmouth to Totnes and then an open top bus return to Paignton. You can do the trip in either direction depending on the state of the tides. This is a good way to see a lot if you are only in the area a short time but both Dartmouth and Totnes deserve a little more time to explore than the schedules allow!