The Georgian city of Bath will take about 35 minutes to reach. An open top bus tour is highly recommended as you can hop on or off at places which interest you.

Salisbury
This beautiful cathedral city is about the same distance in the other direction across Salisbury Plain.
Stately Homes etc.
Bowood House and gardens, Longleat House and Wildlfe Park and Wilton House are all within easy travelling distance for a day trip.