One of the more fun achievements you can earn revolves around finding and scaling the highest buildings. Earning this achievement is reminiscent to being King Kong, particularly since one of the buildings happens to be the Empire State Building. So lets run down the list of what buildings you need to climb to get this prize.
Empire State Building:

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The first recognizable building you get to climb is none other than the Empire State Building. Its silhoutte should be easy to spot, and it really is a nice view from the top. No wonder King Kong felt compelled to climb up its lofty heights. This building can be found in the Lower East Side and should be easy to spot.
Stark Tower:

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The second building you need to find is Tony Stark's home, Stark Tower. Yes, Marvel does allude to other comic book characters in this game, so of course they have to pay homage to where Ironman hangs his hat. This dark and somber-looking building can be found - where else - in Hells Kitchen.
Chysler Building:

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The third building to look out for is the Chrysler building. A majestic ediface of sand-colored stone, you can work your way up its glass-filled sides to peer out over the Lower East Side. You might have seen this one while you were scaling the Empire State Building.
American International Building:

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The next building you'll be looking for is located in the Financial District, namely the American International Building. For those who don't know, this gothic building was the 3rd largest building in existence when it was finished being built. It has been surpassed in height since then, but its easily recognizable as you jump your way through the city.
Trump Tower:

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Last - but definitely not least - is the heavily publicised Trump Tower. This modern work of civilization lies deep within the Financial District, which is not surprising of course. Its still fun though, to climb its exterior and see the world how maybe Donald Trump sees it.
Once you're done climbing the last building, you'll receive the achievement for scaling the top five buildings in the game. You can choose to destroy each one after you scale them of course, which is really fun too. Just make sure you finish climbing to the top before they began to fall down.