Public spaces are well
organised structure designed either by individual, government or non-governmental organisation for any purpose or event like sports, cultural activity or traditional gathering .
Public spaces are sometimes set aside for tourism, political rallies,
religious crusade,etc
The question is, do you think people take better care of public spaces if they find them beautiful?
Response: yes, because it is a special area or space designed for specific purpose as stated already here.
A place like museum there is open space where a lot of people like to go for tourism.
Is caring for public spaces more closely related to their values and culture?
Yes, there's individual levels of manifestation of values, and there's societal levels of manifestation of values.
Values are beliefs that people have about what is right and wrong and what is most important in life. These control their behaviour and promote their culture as the other people would be free to identify with them.
Values are ideas, principles or standards that are needed for the progress and development of individual and society.
The few possible ways that would help people take better care of public space when people imbibe good value system are not limited to these listed but a few;
integrity, unselfishness, fairness, trust, love or patriotism, hospitality, honesty, caring, togetherness, discipline, good manners and sense of good judgement.
If attention is given to what is stated here that way our public spaces would be better cared for.