I'm not sure I have a recommendation, but if I were to look, I would, as you indicated, rule out "Pubs" (Though some "Gastro-Pubs" might fit the bill). With picky eaters, maybe ethnic food, like Indian, Asian, Middle Eastern, or North African might be out.
For an area, SoHo might be an option, many trendy and "up and coming" places set up there.
Looking through a "recommended" listing of recent, the filtered to:
Brasserie Zedel: French Bistro type vibe.
Bancone: Italian with some elegance. Several locations, Pasta centric mains, pride themselves on house made pasta.
Andrew Edmunds: Sort of modern European in old school decor. Daily menu of seasonal items.
I know little about any of these, but the process says they are worth a shot. At least take a look and see if the type of place resonates.
I find Eater and Time Out decent places to look for suggestion, just make sure any articles are recent.