I've read several other questions and answers like this, and most of them say it's connected to your facebook account or something like that.. but my device is not connected to the internet and never has been. So is there anyway when i can transfer my tiny tower progress on to my new device? (which won't be connected to the internet either?) thank you
Yes, IFF you can get internet on both devices. Sign in to Game Center on the "original phone". At some points within the game, it will be saved. In your "new" phone, install Tiny Tower, run it, and when prompted, login to Game Center. It should ask if you want to Restore from the saved game.