I have just installed Xcode 4 and I am trying to create projects that use core data. However, the checkbox to use core data is not available in any of the project templates
As the most upvoted answer of Lindemann says, CoreData is not available for all the project templates. If you wonder why is that, then here is Apple's reason for that.
Important: Not all templates offer a Core Data option. Core Data is an advanced technology that is not required for creating simple applications.
https://developer.apple.com/library/ios/documentation/DataManagement/Devpedia-CoreData/coreDataOverview.html