Panera Bread, well-known for providing freshly baked artisan breads and delicious food made from the highest quality ingredients has GREAT Paninis.
Prices and availability vary for different locations, for instance the prices in the malls and airports seem to be too expensive, but good deals (~$8US) can be found at various locations with great quality and service. They call you by your name. No place in Jamaica compares as yet since they fail to get the bread right, which is key.