Without knowing exactly what you had in mind...there are a few thoughts that I can share....
Romance Traditional:
Hugo's Cellar -
Four Queens : I've recommended this place before, for it's classic, seductive, intimate nature. It is old Vegas, sure, but as elegant and sophisticated as they come. You will need to walk through a casino, on Fremont street, and into a completely different world for your dinner. Classic red velvet, brick walls, and a fireplace greet you, your lady is given a rose, and the waiters and servers have been there since the place opened decades ago.
Piero's Italian -
This place is another classic, rich with an interesting history. It's well reviewed and continues to stack up nationally acclaimed awards for service, style, and cuisine. Everyone who walks in here is treated like family and it's history includes visitors from the Rat Pack to former presidents. A part of "Casino" was even filmed in here.
Casa de Amore -
Another Italian (can't get away from it in Vegas) that just encapsulates everything romance should be. More velvet, candlelight, its own limo, servers in tuxes, and a pianist who frequents nightly until the wee hours of the morning. This is slightly off the strip and again, once you step inside you are like family. A really special Las Vegas tradition that you must visit at one point.
Romance Modern -
The previous posters to this thread have all mentioned exceptional places for more modern romantic environments, and all of the above are exceptional choices I will agree! A couple off the wall places as alternatives....
Romance Eclectic :
Envy Steakhouse -
Not well known as it's in a convention center hotel, The Renaissance. But this steakhouse is one of my favorites and it has won a few awards. Excellent option for lower key, more contemporary romance.
Tillerman -
This is slightly off the strip but wow, there is a huge tree inside that is adorned with white sparkling lights. A complete lazy susan salad tray comes with the meal, and the atmosphere creates the feeling of an outdoor garden party dinner.
Marrakesh -
A Moroccan venue, once inside you the decor is set up just like a traditional Bedouin tent, its exotic and cozy, sitting close on a low couch and eating with your hands. You are served a full 7 course menu, complete with music and entertainment. (this would be traditional belly dancers, make sure your lady wouldn't mind sharing her evening in this sort of environment )
Sorry for the dissertation but these should give you a few different options. I'd be more than happy to answer specific questions, just send me a PM!!!