The South Devon coast is well enough known and most people recognise that there is a national park on Dartmoor - even those who have not seen it. It might come as more of a surprise to know of the wonderful lanes and river valleys between the two but certainly those with families will be doing the children out of major delights if they are not taken to explore the river valleys and some of the country lanes in the primrose season have to be seen to be believed. Plymouth's boundaries have stretched well out to swallow what I remember as country so I will ont be too specific about where to look but get a decent map and search for minor rural lanes in hte area south of the moor and you will find primroses and violets galore in season.
Other spring flowers are profuse around Miltoncombe and Buckland Abbey near Yelverton. [Plymouth-Tavistock road]
As for the wooded river areas, try some of the following [* means a particularly high recommendation.]:-
West to East: River Tavy - round Bere Ferrers; meeting with Walkham at Double Waters*; Tavistock: River Walkham: Walkhampton Chursh - you can probably go up the tower: River Meavy: Burrator Reservoir*; Meavy and Sheepstor villages; junction with the Cad at Shaugh Bridge* to form the Plym: River Yealm: Cornwood; Hawns and Dendles wood* River Erme: Harford*: River Avon; Shipley Bridge and Avon Dam.