The beauty of exploring forgotten places is that it can be done anywhere--even the big city. My time in New York City introduced me to some historic places. I've seen the remnants of an old fort along the coast of Staten Island on a Coast Guard facility. Another interesting fort is still part of an active Army post. Then there were preserved buildings from as far back as the Revolutionary War.
Other more modern properties had fallen into disrepair, such as the old mental institution on Roosevelt's Island in the East River or the old buildings down under the Manhattan Bridge.
A guy named Kevin Walsh has created an incredible resource about some of these sites, along with many, many more at Forgotten NY. He's got in-depth information about all sorts of history that's hidden in plain sight in the city--old advertising, old streetlamps, abandoned airports ... you name it. Of course, there are some sites, such as abandoned subway stations that aren't in common public view.
One old train line, the High Line on Manhattan's West Side, is especially out of place. It's an elevated train track, which is unusual in Manhattan (and has been for probably near 100 years). The so-called Outer Boroughs still have elevated subway lines in places. The High Line can be seen along the West Side Highway, with grass and trees growing from the abandoned track bed. Walsh's site has information about the line, which some in the city want to see made into a linear park.
Philip Eoute, who blogged about his semester-long tour of the Midwest, also tipped me off to a blog, which has more photos of the High Line in its current state.
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Disclaimer: When I speak of exploring forgotten places, I do not mean trespassing or taking what my family calls "foolish chances."