Public Spaces in The Sims 4 can not be edited by the player. SimGuruGraham confirmed this today on Twitter. Public Spaces are not to be confused with Residential and Community lots, they are areas with objects in them that Sims will use, such as park objects.
@Weealbet @Inge_Jones @SimGuruSarah Sorry no, I have not said that. The public spaces of a neighborhood are not editable.
— Graham Nardone (@SimGuruGraham) June 18, 2014
@theBloomie You can still edit all community lots and venues the same way you've always been able (cont) http://t.co/HPNEaO8T5j
— Graham Nardone (@SimGuruGraham) June 18, 2014
Click here for the full Tweet
@whoooisv They can be either one. We have some parks in public spaces, as well as dedicated park lots.
— Graham Nardone (@SimGuruGraham) June 18, 2014