My favorite if Bassett's of Philadelphia.

Hard to find in NY, but if y0u're in downtown Philly they've got a stand in the Reading Terminal Market.

Two flavors to die for: Butterscotch Vanilla and Marshmallow Chocolate. (Like Ben & Jerry's there's no skimping on the mixed-in flavors but Bassett's is smoother and they don't insist on encumbering, like B&J, practically every variety with chocolate chunks.

In terms of the soft variety, NYC's long-gone Prexy's.

Known for their hamburgers (from fresh, not frozen patties) grilled from scratch (slogan: "The Hamburger With A College Education") their soft-serve (only flavor, vanilla) was the softest, creamiest, richest soft ice cream I ever had (last time had to have been over thirty years ago).