The world is undergoing rapid urbanization, and it is presumed that by 2050, almost 66% of the children's population will be found in cities. The well-being of children is associated with their day-to-day surrounding environment, which includes their home, school, and recreational spaces. Children's active participation in open spaces is critically necessary for their physical, social, emotional, and cognitive well-being. Urbanization is putting pressure on the quality and quantity of open spaces, where crowding, maintenance, and stranger-danger are persistent concerns of the parents for their children's outdoor play experience. A survey was conducted in the city of Pune with 105 children, studying their perception and use of open space. Children were asked to prepare cognitive maps indicating fear factors and/or elements found in the open spaces which they visit regularly. Children indicated various fear perceptions factors like strangers, unclean surroundings, diagrams related to the upkeep of various elements in open spaces. The coding of the diagrams indicated concerns related to safety from crime, injury from harmful elements, wayfinding, etc. The perception of children was analyzed using qualitative methods. Further, the paper discusses the fear factors associated with open space aspects like design, aesthetics, density, accessibility, traffic, etc., which contribute to children's perception of open spaces, thus affecting children's independent mobility, the choice of the space of play, and the amount of time spent during outdoor play. Getting parental license to go outdoors was related to the Natural surveillance available, and the fear factors were found to be related to the space management aspects like fencing, maintenance, and also security in case of strangers present in the spaces.