At just under an hour's walk from Bristol Temple Meads and through Bristols historic street, the Clifton Suspension Bridge is well worth the stroll. It is widely considered as one of Isambard Kingdom Brunel's masterpieces of industrial design and spans the impressive River Avon gorge.
If you don't fancy the walk from Bristol City Centre there is a good bus service running directly from the station. Look out for bus numbers 8 or 9 which run every 15 minutes during the day.