A much belated congratulations on your wedding, Neo.

Also agree about the tasting menus. Although for someone who does like them (the OP?) a place to put on the list would be ATERA on Worth Street. Very creative; mostly counter seating.
Tasting menu of 20 courses; expensive. Seats only 18 diners. Beautiful space; casual dress ok.

http://ateranyc.com/



Agree about the Babbo comments, too. Their food is very good, but the restaurants is not in the class of Jean Georges, Le Bernadin, etc. I'd eat there more often for a casual dinner, though, if it were not so difficult to get a table. But I would not put it on the list for someone with only a few nights in the City.