Having moved to Seattle from New York, I was initially dismayed by the lack of pizzerias making good NY Style Pizza. However, I have found one place that truly qualifies as a good NY Style pizzeria, Piecora's Pizzeria on E. Madison on Capital Hill. With puffy outer crust, tapering to a thin, crisp middle, topped with lots of great tomato sauce and an abundance of cheese, Piecora's pizza has found a solid formula. While it is not Ray's in NY, it is the closest thing I have found in Seattle.
While I usually get Piecora's to takeout, they have a restaurant with salads, beers on tap, etc. It is sometimes a bit smoky for my tastes.