of these 4 choices, what is the overall best nyc experience for a couple:
Blue Hill (first) and Gramercy Tavern (second).
BH has cozy and romantic decor, and the food is outstanding -- more sophisticated and well executed than GT. Seasonal, farm-to-table dining with one of the more (relatively) affordable tasting menus in the city. That said, you won't go wrong at GT, with its warm service and more comfort food-y offerings.
Been to Little Owl on several occasions, each time increasingly disappointed. At this point, it's off my list. Yes, it's on an adorable street in the West Village and yes, it's got that tiny, boxed-in, "I'm in the heart of it all" feeling. But you will feel ripped off given the amateur hour cooking and brusque waitstaff attitude (although I haven't been in months so there may be some positive turnover in this respect). See my last post on this place: http://chowhound.chow.com/topics/235023 (but do note that it's from Jan 07).
Never been to Le Gigot.
I've not been to Little Owl or Blue Hill. And, while I've not been to Gramercy Tavern since the new chef arrived (at least a year ago now), there are many favorable reports about it. We've only gone to the Tavern Room in front, which doesn't take reservations, but it's not usually much of a wait. The room is always incredibly beautiful, with seasonal flowers etc., and has been one of our NYC favorites (so I'm not sure why we've not been back for so long!).
Haven't been to Le Gigot.
I think the food and service are stronger at GT, as is the service. It is a big space with high ceilings and feels more like a "temple of cuisine" than Blue Hill. I've been to Blue Hill on many occasions as well and it's a bit more "intimate" - meaning darker and tables closer together. "Cozy" is the right word.
Little Owl is a different sort of thing altogether - more of a "neighborhood gem" than a high-end restaurant. It is certainly cramped (or maybe "cozy", but it's a heck of a lot more "cozy" than Blue Hill) and almost impossible to get a reservation. I would respectfully disagree with the earlier poster with respect to the food - in the few times I've been there I've found it to be delicious, straightforward Greenmarket-driven American cooking. It is not a gourmet restaurant like BH or GT, nor it it priced like one. Service will be more informal and the wine list is significantly truncated. Besides being more cramped it will be louder. So it depends on what a couple wants I suppose. Some nights, you want want a fancy dinner for two. Sometimes, you want comforting, well-executed food and maybe a hint of feeling transported, which I think Little Owl can give you. I wouldn't reject any of the three places out of hand; they are all very different.
Blue Hill, in any contest but especially if you want a first-class meal for two in an intimate setting.