As the name implies "public space" is meant to be for the whole "public", but of course it's not that simple. Whether through physical design (facilities) or social design (the people), we do sometimes feel uncomfortable in spaces. There are groups that can often get marginalised in public urban spaces (eg cyclists, homeless, youth, elderly disabled etc) and there is a whole amount of literature and research on these issues. Example - YSpace on youth, Parity on homeless.
Enrique Peñalosa talks about how good cities that are safe for children, the elderly and handicapped are more likely to be good for everyone else too.
Think about who you are designing your PARK for.