I looked around for a mailbox.

Literal

Mailbox [object-を] searching surroundings [object-を] looked-around.

ポスト ('mailbox') is a loanword (from English 'post'). 探して ('searching for') in て-form chains to 辺りを見回した ('looked around the area'). 辺り (あたり, 'area, vicinity'). Subject omitted.