My first advice would be to do what my wife and I decided to do years ago. Give each other promised rain checks for a Valentines dinner on another night. Less crowded, better service, and often cheaper prices
That aside, "romantic" varies greatly by person/couple. While many of the suggestions already made are good, depends on what you are looking for.
As an example, many often mention Mise en Place. I very much like to go there, and would recommend it. But wouldn't fit my definition of romantic. The room is too open, non-private for my tastes.
Having said that, I would include "The Restaurant". While it also has a large, open, crowded space, there is something about the atmosphere of the room that my wife and I both like. With a fire in the fireplace at this time of year, it would work for us. (Though we haven't been there since the personnel turnover discussed here)
Haven't been there in many years, but assuming it hasn't changed, I'd agree with the many votes for the Woodshed.
Surprised no one has mentioned Lyon's Den.