Cadbury garden centre, lots of play cafes in Bristol, be weird be wild be wonderful, the curious in hanham, wild things in wilsbridge, little town in chipping sod bury, wacky warehouse in Emerson’s green and longwell green
Tots and teapots is perfect for babies and there's soft play but it's small and not too manic (like the bigger soft plays)
Mamas hub in Bradley stoke has a baby room and sensory room, they also run specific baby sessions.
Super Sense at the Imperial Sports Ground is also good
Skyboat cafe in Redland has a baby section