There are lots of cider pubs in Bristol. Three I visit are, the Apple Tree (27 Philip Street, Bedminster), the Barley Mow (1-3 East Street, Bedminster) and the Long Bar (70 Old Market Street Old Market Bristol ).
The Apple Tree is a tiny old fashioned pub, serving Taunton Traditional. Full of characters and well worth a visit.
The Barley Mow also sells Taunton Traditional, is always full and lively.
The Long Bar sells Thatcher's Traditional and Cheddar Valley cider. Rough and ready crowd.
http://www.ukcider.co.uk/wiki/index.php/Cider_Pub_Guide_to_Bristol