A Pythagorean funhouse that tries, successfully, to prove that math is the coolest thing ever.

Hidden in Central Park's Ramble is a troublesome cave buried just beneath the surface.

The feral felines of Roosevelt Island have a small army of allies and an abandoned hospital all to themselves.

Elevated freight railway turned wildly successful urban park.

This lower Manhattan bar is set up in an old bank vault that rests beneath a skyscraper that hides even more historic splendor.

A miniature rainforest is growing inside of a Midtown Manhattan office building.

This abandoned subway station beneath the Waldorf-Astoria hotel is allegedly used to secretly transport presidents.

Manhattan’s Battery Park has a whimsical carousel full of spinning, glowing fish.

This beautiful building in the heart of Manhattan's Financial District was empty for decades.

Dodge prohibitionists and slide through the telephone booth in Crif Dogs.

Try not to get slimed in Tribeca.

The oldest family-run luncheonette in New York, last renovated in 1948, still serves food and drinks the old-fashioned way.

Amid the bustle and noise of the Financial District hides a secluded garden oasis above the city streets.

A crumbling hospital from the 1850s on Roosevelt Island.

La Monte Young and Marian Zazeela's "Dream House" will immerse you in an ever changing world of sound and light.

A beautiful and abandoned New York subway station from 1904, complete with chandelier.

The world's first combination ski slope and power plant.

Visitors are treated to a stained glass kaleidoscope interior inside this work of art.

A little-known cafe in an old copper bridge tower with 360-degree views of the harbor.

The old observatory in Copenhagen has a spiral corridor used as a racetrack.

Pre-Nazi swastikas adorn the sculpted pachyderms flanking this brewhouse portal.

Opulence and fantasy collide in this royal chair which is supposedly made with unicorn horns.

Danish tourist destination well known for open stalls where vendors sell marijuana on the street.

Hans Christian Andersen for the postmodern world.