A car opens up some of the best of Somerset and Dorset within an hour of Glastonbury.
Wells, six miles north, is England's smallest cathedral city — a 12th-century cathedral with the famous scissor arches, a moated bishop's palace, and a market square that has changed little since the Middle Ages. Easy by car or the 376 bus.
Cheddar Gorge, about a half-hour drive, is the deepest gorge in Britain, cut into the Mendip Hills. Walk the rim path for the best views, then visit the show caves at the bottom. Cheddar village itself is touristy but the cheese is the real thing.
Stourhead, an hour to the east, is one of England's finest 18th-century landscape gardens — a circular walk around a lake punctuated by classical follies and bridges. National Trust property; busy on summer weekends.
Wookey Hole, just north of Wells, is a series of limestone caves with a famous Iron Age legend of a witch. More family-friendly than scientific, with paper mill demonstrations and a small museum.
Bath, an hour to the north, is overkill for a day trip if you have only one — but the Roman baths, Georgian crescents, and the Holburne Museum all reward the journey.