We have a shared family computer running Windows 7 Home Premium (x64). Is it possible to set the Public folders so that kids can create and modify their own files & folders within that tree, while everything else in the tree is read only?
The simplest configuration is to allow the Users group to
Children will always automatically have full control on objects (files and folders) they own or create.
You can specifically set a file, or groups of files, to be read only to everyone but you, while the folder they're contained in is both read and write. That way, your files are able to be read, but not edited, and your kids can still add their own files.
Make your files/folders read only, as shown below, but the overall folder read/write.
I didn't include my file permissions because it lists my full name, but when changing the permissions for a person on your computer, you should be able to choose 'Allow' or 'Deny' in each area below.
Right-click file -> Properties -> Security tab -> Advanced: From here you should be able to edit the access abilities of each member of your family, or you could create a group as grawity has suggested and put your kids into a group and then give that group certain permissions.