I posted last night under the subject of "Good romantic Manhattan restaurant that's not OVERLY expensive for LA hound and my soon to be fiancee."
I got some excellent suggestions. I've pared them down to those I mention in the subject heading.
I made a reservation at Babbo because, from what I've read, it seems to be the most difficult place in which to get a seat (as it is, we have a reservation for the very-late-by-LA-standards time of 10:45 on Tuesday). I still may change my mind, but for the moment that's most likely where we will end up-- that is unless some NY hounds want to talk me out of it. (It's not a particularly romantic spot, is it?)
Thank you to all of the posters that made recommendations. I will post about the meal, wherever it ends up being, sometime next week.