In iOS 7, the document directory of the iOS simulators can be found in:
/Users/Sabo/Library/Application Support/iPhone Simulator/
However,
Based on Ankur's answer but for us Swift users:
let urls = NSFileManager.defaultManager().URLsForDirectory(.DocumentDirectory, inDomains: .UserDomainMask) println("Possible sqlite file: \(urls)")
Put it inside ViewDidLoad and it will print out immediately upon execution of the app.