The phrase 'gad about' has a light-hearted, informal feeling, suitable for casual conversations. They love to gad about the city and explore new cafes.
Pro Tip 2/3
Leisure Activity
'Gad about' implies engaging in activities for enjoyment, not for work or obligation. On weekends, I prefer to gad about the countryside.
Pro Tip 3/3
Frequency
When you 'gad about,' it suggests that you do so often and to various places. Ever since she bought a bike, she's been gadding about town daily.