Times Square is fine well into the night if you don't look like an easy mark. NYC characters might approach you but just keep walking. Don't stare at your phone or be drunk and walking back to your hotel at 3am. So much bad news about the trains these days. If there's calm people on a platform, you can be calm too. If you're alone or don't like something you see bail and grab a cab. Or just take cabs after 11pm. I'd skip the statue, takes too much time plus as said it will be cold.