Blenheim Gardens Minehead - Free
If you love a picnic, there is nowhere nicer than Blenheim Gardens on a sunny day. Just off the main town centre, enjoy the beautiful 6 acre landscaped gardens, find shade under a leafy tree and play a round on the 18-hole putting course. On a weekend in the summer, stay all day for entertainment in the bandstand and have food, drinks and ice creams from the cafe
https://www.facebook.com/BlenheimGardens
Hestercombe Gardens, near Taunton - entry fee
Forty acres of woodland walks, cascades and temples, vivid colours, formal terraces and views that take your breath away. A unique combination of three period gardens: the Georgian landscape, Victorian terrace and formal Edwardian garden.
Walled Gardens of Cannington - entry fee
Located in the village of Cannington, Somerset, The Walled Gardens of Cannington lie within the grounds of a medieval priory and many of its fine buildings, including the walls of the garden, remain.
http://www.canningtonwalledgardens.co.uk/home/
RHS Garden Rosemoor, Great Torrington, Devon - entry fee
An enchanting 65 acre garden, inspirational no matter what the season with over 130 annual events, workshops and courses, restaurant, plant centre and gift shop.