Mostly known these days for the gigantic music festival which happens just down the road, Glastonbury the town is fascinating in its own right. The Tor, with its ruined church (now owned by the National Trust) and the myths that have grown up around it, attracts all sorts of people. Druids, pagans, Wiccans, new age-ers, mystics, and, of course, a few hardy tourists.
The Tor is variously touted as Camelot, a meeting of Ley lines, an ancient monument, and just a lumpy bit of ground with nice views, but the culture that has grown up around it is what makes Glastonbury the town so interesting. The High Street plays host to a multitude of wonderful vegetarian cafés, crystal shops, eco-friendly grocers, second-hand/recycled clothing boutiques, and the odd armory. All of this is crammed together with the standard Somerset High Street quota of charity shops and newsagents.
Wandering around the town you can really see how normal life interfaces with the occult. You'll find Church of England sites next to Buddhist Temples, coaches full of OAPs visiting the abbey for a cream tea and road-weary pilgrims busking for falafel money, Moms on the school run and gypsies selling lucky heather. If you're not sure where to go, the Tourist Information Centre is a good place to start.
Be sure to explore all of the little courtyards and exotic smelling shops and take the trek up the Tor - worth it for the view alone. For something more sedate try the Rural Life Museum where you can learn all you ever wanted and more about agriculture. And if it's all a bit too weird for you, there's an outlet shopping village just next door.