Port Authority of New York has a monopoly on all bridges built within 25 mile radius of the Statue of Liberty. The Tappan Zee Bridge is just north of that radius. The New York governor Thomas E Dewey rejected the Port Authority's competing proposal to build a bridge closer to NYC and proceeded with building his own bridge that would be part of the New York Thruway. Dewey needed the revenue from the tolls for that bridge to pay for the construction of the Thruway and didn't want it to go to Port Authority.

Source: http://www.npr.org/blogs/money/2011/08/19/139749870/a-big-bridge-in-the-wrong-place

Check out episode 297 of NPR's planet money podcast http://www.npr.org/blogs/money/2013/01/01/168361673/episode-297-a-big-bridge-in-the-wrong-place

They tell the wholes story and it's actually quite fascinating.

Please bear in mind the topography of the surrounding area. While the Hudson has a very murky bottom and can be quite wide, the area also has many rocky outcroppings such as Palisades cliffs. Not every location is suitable for building. There's also an abundance of historic landmarks in the area that you wouldn't want to destroy.

The design of the bridge was a submerged pontoon causeway for most of the structure, this design needed the slow current at the point it was built to withstand the current. The replacement bridge is using conventional piles for the causeway section. Rumor also has it that Dewey hated Robert Moses the master NYC developer and wanted to take it out of his jurisdiction.