If you were playing logged into Game Center on the old device you can simply login to the same Game Center account on the new device and then download the Tiny Towers app from the App Store. When you open the app and it connects to Game Center, It will attempt to load your latest saved game. Please allow a few minutes for the restore prompt to come up.
Alternatively, you can restore your game from a recent iTunes or iCloud backup from your old device. Please see Apple's how-to guide for more information on backing up and restoring:
Note: There is a check in the backup system that prevents a smaller tower from overwriting a larger tower. This is to protect players from losing progress. If you have reset your tower at some point and the new tower is not taller than the old one, your newer tower wont overwrite your old tower on the backup until it surpasses the old one in height.