We've recently implemented a transfer method so you can continue playing on a new device. Here are the steps:
1. Make sure your current hotel is connected to Game Center via the neighbor menu.
2. Put Pet Hotel on your new device and play until you are level 6 and unlock visiting neighbors with Game Center.
3. Connect to Game Center in-game using the same account as your old device.
4. Tap the gears button in the bottom right corner of the game then 'Load Hotel'. This will load your hotel from your old device.
If you run into any issues, please contact us at email@example.com. Also, getting to level 6 first is an unavoidable inconvenience but it shouldn't be too long before you are back at your old hotel. Enjoy!