Correct answer✅:
a) We spent the day wandering around the city.
🔖Wander /ˈwɒndə(r)/
to walk around slowly from place to place, in a relaxed way, especially without any clear purpose or direction
b) I am wondering if you could help me.
🔖Wonder /ˈwʌndə(r)/
to think about something because you want to know more facts about it
Easy English by Vesna 