Lots of good suggestions, and you'll get even more the longer the thread goes on. I agree with a couple of other posters that a romantic setting can be had in many places and that the most important factor is your partner. Still, it's worth adding my two cents' worth just because I like romantic dinners.
Artist Point: One of the top two quietest of the Signatures. The ambiance is serene, and the setting outside around the Lodge is wonderful--flickering lanterns, majestic music, and walking down the various paths after a meal is wonderful treat. The food, service, and wine list are topnotch. I suggest securing either an early ADR or a later ADR and ask to be seated at the window. Your views will be excellent.
Jiko: The other of the two quietest Signatures. Much of what I said about AP can be said about Jiko--lovely ambiance, great food, excellent service, and a locale that's hard to match.
CG: I offer this only if you don't mind a lot of ambient noise and if you want to watch HEA from there. The food is generally superb, though pricey even for a Signature, but there is a level of revelry in CG that makes it mildly off putting if you want a more intimate dinner.
Tutto Gusto Wine Cellar: While I might not try it for dinner, it's an exceptional spot to have a quiet, romantic lunch or afternoon snack. . .if you time it right. It's a small place, and they don't take ADRs, but if you get to them when they first open, there is a small alcove with a few small couches and coffee tables that is perfect for a cozy meal. They have a solid wine selection (and bar offerings), antipasto plates, cheeses, and even dishes that can be ordered from Tutto Italia next door.
BiCE: Okay, this one is off campus and over at the Dark Side. However, it's definitely worth the 15-20 minute drive. The menu has divine selections; their wine list is extensive; and the setting is quite upscale without being snobby. Il Mulino used to be the place where we most enjoyed Italian dishes at the World, and we still go there; however, BiCE is a step up. Do a little research on the menu and see what you think.