By default, access rights are granted to allow all authenticated users to create places, and delete the places they create. It is often desirable to limit the set of users allowed to create or delete places. Access to create a place is granted according to the user's access to templates. If the user has no rights on any templates, they will not be able to create any places.
You can restrict access on the "Application Template Root", the container for all templates, and have it inherited down to all the templates. Go to Site Administration > Advanced Administration > Resource Permissions > Application Template Root > click Assign Access > click Edit Role for the User role > Delete the All Authenticated Users entry. Add whatever users/groups you do want to be able to create places. You can do this on individual templates on the "Manage Templates" page too.
To hide the "Create a Place" and other similar buttons, go to "Site Administration > Advanced Administration > Portlets > search for "Quickr My Navigation" > click Assign access" > uncheck Allow Inheritance on the User and Priviledged User roles. That will hide this entire portlet pictured below. Add back in as the User role any users/groups you want manage/create places.
Changing the access list on the templates first will change the actual access control. Lotus Quickr includes REST APIs that a malicious user could call if you just hid the options in the UI and didn't actually restrict the access control. Setting the access list on the portlet will simply hide the options in the most visible user interface to avoid leading the user down a dead-end.
A user could still become a place owner or manager by having that role explicitly assigned to them by a place owner, but setting access lists as detailed above will prevent a user from being able to create any new places and will hide the most visible user interface for place management from the user.