In 2001, Todd English’s Olives NY, in the W Union Square Hotel, was the place to go, especially if you were looking for a scene out of “Sex and the City” to accompany your chestnut ravioli with venison Bolognese sauce, washed down with an Appletini.

Of course, times change and hot spots dwindle, but Olives held on for longer than many—around 13 years.

In...