Moto would be a good option for you, I think. The food is memorable, to say the least. The atmosphere is formal but the food is so playful that the restaurant is far from stuffy. I've been there twice, once with another couple and once with my wife and mother-in-law. Both times we had a lot of fun and never felt that we had to keep our voices down. Perhaps we offended people, but I doubt it. There is no chef's table at Moto.
Schwa would be another good option. If you can get them on the phone and secure a reservation. Great, great food, as documented on many posts on this site. Not formal at all.
It is a bit out of the way, but Arun's might satisfy your wishes, too.
Other options: Spring, Custom House, Boka, and Le Lan.