There are two round trash cans to the right of the Underground Tour entrance. Dig through the open trashcan (the one on the right) and at the very bottom, you will find a pair of tickets.
You cannot use them, however. You must return them to their owner, who is at the Web Browser internet Cafe.
(see related question)
you go in the underground cave but first you need to get the tickets.
The can with the tickets is the round one just to the right of the Underground Tour entrance.
You return them to the guy in the internet cafe.
it is in the underground at counterfeit
You can look around the island all you want. The "Underground Tunnel Tour" requires tickets. (see related question)
The tickets to the Underground Tour on Counterfeit Island are at the bottom of the round garbage can to the right of the entrance. Once you have them, you have to return them to their owner, who is at the Web Browser Cafe on main Street.
Recover the Underground tickets from the trash can near the underground entrance, and return them to their owner at the Internet cafe. There is nothing you can do about the balloon boy.
representative government
There is no safe on Counterfeit Island. There is an underground hatch that has a Dragon Face lock on it.
The trash can you find the Underground Tickets in is already open : it is the "right" one of the pair to the right of the Underground entrance. (Just paw through the refuse to the bottom.)
You can find two tickets to the Underground Tour in the two trashcans to the right of the entrance (dig to the bottom). Once you have gone to the Countryside with a green balloon, you can return the tickets to their owner at the Internet Cafe on Main Street.
Once you have returned the tickets to the man who lost them, use the one he gives you. (see related question)