Stanton Drew is great - you should go.
There is also a ruined Iron Age hillfort in Leigh Woods (Avon Gorge) if you like that sort of thing (which I do).
If anywhere is going to be muddy this time of the year it's Leigh Woods....I would suggest Stanton Drew as the best bet...you don't have to go right across the field to see them if you don't want to and the cove is beside the pub.