Barrington Court

Echoes of the past haunt this now empty Tudor manor house, so lovingly restored in the 1920s by Sir Arthur Lyle. Old farm buildings host a pottery and woodcarver, both of whom sell their wares. What were once cow yards, pens and fields have been transformed into fragrant and delightful flower gardens, their design influenced by Gertrude Jekyll. The stone-walled kitchen garden produces a variety of wonderful fruit and vegetables, which can be enjoyed in the restaurant, while the orchards provide the apples for our own cider and apple juice. This is a place to relax and refresh the senses.

http://www.nationaltrust.org.uk/main/w-barringtoncourt

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East Lambrook Manor Gardens

One of the best-loved privately owned gardens in England created by the late Margery Fish, celebrated plantswoman and gardening writer. Her natural gift for combining old-fashioned and contemporary plants in a relaxed and informal manner has created a garden of immense beauty and charm. The Grade 1 listed garden is renowned as the premier example of the English cottage garden style and is noted for its specialist collections of snowdrops, hellebores and hardy geraniums.

http://www.eastlambrook.co.uk/pages/

Montacute House

Montacute House is a magnificent, glittering mansion, built in the late 16th century for Sir Edward Phelips. There are many Renaissance features, and the Long Gallery, the longest of its kind in England, displays more than 60 of the finest Tudor and Elizabethan portraits from the National Portrait Gallery collection. The state rooms display a fine range of period furniture and textiles, including samplers from the Goodhart collection. Montacute’s formal gardens are perfect for a stroll and include a collection of roses, mixed borders and famous wobbly hedges. Waymarked walks lead around the wider estate, which encompasses St Michael’s Hill.

http://www.nationaltrust.org.uk/main/w-vh/w-visits/w-findaplace/w-montacute/

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Muchelney Abbey

Muchelney Abbey, which lies 2 miles south of Langport, was once a landmark in the Somerset Levels and still has much to offer its visitors – history lovers in particular will enjoy this fascinating site. It was once a wealthy Benedictine house and the second oldest religious foundation in Somerset, but as part of the dissolution the abbey’s principal buildings were demolished by Henry VIII in 1538. Visitors can still see the clearly laid out foundations of the abbey, parts of the richly decorated cloister walk and thatched monks’ lavatory- the only one of its kind in Britain. The 16th century abbots’ house remains intact with its magnificent rooms, and site finds are on display illustrating monastic life.

http://www.english-heritage.org.uk/visit/places/muchelney-abbey/

Also close by 

Haynes Motor Museum
Fleet Air Arm Museum
Clarkes Village, Street
Glastonbury
Wells Cathedral
Wookey Hole
Cheddar Gorge
Burrow Hill Cider Farm