peer, pier

Peer or peer means to look at keenly or closely--
She would peer at the neighbors from behind the curtains.
Without his glasses, he seemed to peer at people with a look of suspicion.

Peer also means an equal, often used to mean the equal of a titled person or lord, as in England--
The queen named him a peer of the realm.
The British still retain the right to be tried by a jury of their peers.

Pier or pier ( rhymes with peer ) means a walkway or structure  built over the ocean or a river--
They built an amusement park on the pier.
They liked to stand on the pier and look at the ocean.

Now that you know that, you can say--
"She would stand on the edge of the pier and peer at the river, looking for boats."

Note--"appear" means to come into view--
"when what to my wondering eyed should appear..."
Not to be confused with "a pier", a structure built over the water--
They planned to build a pier on the riverfront.
Not to be confused with "a peer", meaning an equal--
The veterans considered him a peer after two years on the job.