What can I do in the Post Office?

Not send a letter, regrettably.

You can relax in the yard, and gaze up at the Clock Tower if you like.

You can also open a specific post box once you find the key.

Come back when you manage to get a key from the Curiosity Shoppe.

The hint on which box to try and unlock is in the To Do list on the DESK.

Use the KEY from the Curiosity Shoppe on box 11.

Empty the box of its contents.