We are local to Torquay.
Greenway is wonderful and an absolute must but, if going by car, you need to book parking as it is very limited.
Torre Abbey on the seafront (English Heritage) has not long ago been refurbished and is extremely interesting. There is Agatha Christie information there.
Cockington Village, just a mile or so up the road (walkable from the seafront), is beautiful with a lovely pub, tearoom and shops. You can also ride in a horse and cart.
The Grand Hotel right on the front has a lovely old-fashioned lounge overlooking the sea and is open to the public for coffee, tea and cake.
The theatre, on the seafront, has good varied entertainment as does the theatre in nearby Babbacombe.
All in all, the seafront is lovely but don't bother with the town itself as it is run down.
Torquay is an excellent base for the whole area. Have a wonderful time.