For my wife and I, we celebrate both Valentine's Day and the anniversary of becoming a couple (as opposed to being married, which is later). Generally, 95% of all Valentine Day restaurant experiences are horrid. Most restaurants do over-priced, dumbed down menus with very limited options.
To change things a bit, we agree to celebrate the day before or after. Also, I do theme events. For example, this year, we are doing a progressive dinner - each stop has the unifying concept of being a "bar" - but not for drinks (think, e.g., sushi, tapas, oyster). In other years, I had done a scavenger hunt. In prior years, we have had different themes.
As a rule, I plan the day or evening and surprise my wife. My experience is that most women appreciate the effort if one does something that demonstrates a bit of planning and does not seem to just be a pre-set dinner.
Some less predictable romantic spots in and around NYC:
The Cloisters followed by a quiet brunch;
Ice skating outdoors in Brooklyn;
a country inn in Westchester or Putnam counties;