Your'e going to start something here as it depends on what rings your bells and how far you want to go. Your best bet is to call up the map browser, home in on the relevant area, and see what comes up ;)

yep, stanton drew is a must ( poo pongo field as my girls call it....watch out for the cow-shit), my folks now live v near brent knoll & i've been meaning to climb it for a few years,but never seem to get round to it

priddy circles,too, if you have a car - ask Pete G nicely....wookey hole

a go-kart track & a decent greek restaraunt in town

when are you going?

If you are doing all things ancient and antiquarian in Somerset you could call in on my parents!! :o)

If you want a super duper fantastic photographic panoramic view of the Somerset Levels, Barrow Mump, Cadbury Castle, Glasto Tor and all the way to Clay Hill and then on forever then take a trip to Ham Hill, tis an old quary site and iron age fort and the views are absolutely breathtaking!! http://www.ham-hill.co.uk/ then you can call in on my parents for tea!!!

Stoney Littleton at Wellow, near Bath is one of the best and more peaceful longbarrows within driving distance of Weston.
Also, in Bristol, is a site I have yet to visit - a small burial chamber in the Garden of 59, Druid Hill, Druid Stoke, Bristol. An OLD local history book I have seen says that the site "May be inspected [..] at reasonable times" I really don't know what the situation is with that now, or even if it is still there. I really should go and look for myself.
Good luck