A free day in a city, with no bookings, is a skill. Without a list you either walk in circles near the hotel or panic and open a guide. There is a middle. Give the day a direction and let the streets fill it in.
Pick a direction, not a sight
Choose a river, a ridge, a market street, or a park edge, and walk that way for an hour. Turn when something is louder than the plan. A church door open, a queue that smells like food, a view at the end of a side street. You are not lost if you know which way the hotel is. You are travelling.
Eat when you are hungry
Do not save lunch for a famous place you might not reach. Eat the good ordinary thing in front of you. A free day collapses when you are tired and still hunting for the right cafe. Sit down. The afternoon improves immediately. If you want one deliberate stop, make it the last, on the way back, so the morning stays loose.
Stop on purpose
Go back while you still like the day. A free day with no list should end before your feet file a complaint. You will not have seen the official highlights, and you will have seen the city anyway. That is what the empty page in the plan was for.