^It gives them an excuse to not have regular business hours so they can spend all day holding hands in Central Park on a Wednesday.
New York is a beautiful and glamorous city, with a lot of character and a lot of interesting shooting locations. It has a famous skyline recognized around the world, and in a sense it's not just "America's Informal Capitol", it's "The Capitol of the World". When a foreigner thinks "American city", they can't help but think "New York".
There are always people and cars moving around, so it always feels alive, and it's a city of many cultures where almost anyone working in any profession could live, from bricklayer to artisan to banker. It's also a city that is very friendly to motion picture development and there is a very professional and skilled workforce in the area.
And I'm sure if we really put our heads together, we could think of plenty of romantic movies that take place in American cities other than the US. "The Graduate" took place in San Francisco, for example. "An Officer and a Gentleman" took place in Washington state.