If there's no in-app option to reset your Pet City game, I'd suggest removing the application from your Facebook and then re-adding it. This usually works to clear the data and allow you to start afresh!
How To Delete A Facebook Game
- Click the cog icon in the top right.
- Click "account settings" from the drop-down menu.
- On the next page, scroll down to where it says "apps" on the left.
- Find the app you want to remove—in your case, Pet City.
- Click the little cross next to the app.
- You'll get a little box come up, asking you if you're sure you want to remove the app. Click "remove".
To re-add the game to your Facebook, search for it in the search bar and click "go to application" when you find it.