Key West is full of historical landmarks, interesting places to visit, and museums. The beginning of Route 1 sign, to me, is a landmark. I live at the other end of Route 1, approximately 1600 miles away. I've traveled on it all my life. A route marker for a highway might not be a landmark in the strictest sense, but I enjoyed finding it.
There are many beautiful old Victorian homes in Key West. Many of these have become B&B's for the tourists. Driving along the streets of the old town you will see lots of them. A few of the more famous homes are open for tours. The Southernmost House, President Truman's Little Whitehouse, and Ernest Hemingway's Home and Museum are a great way to spend a few hours in Key West.
Just a block or two from Hemingway's house is the old lighthouse. A few blocks away is the Audubon House, which has a library of original drawings that Audubon did while in Key West.
The most photographed landmark of Key West is probably the southermost point. It is the marker for the furthest south you can be in the continintal U.S. and sets exactly 90 miles from the shore of Cuba.